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2013-02-08T16:08:46Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 ]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 ]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 ]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 ]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 ]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 10 ]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 11 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 12 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 13 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 14 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 15 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 16 ]]

[[File:Data.JPG|thumb|right|250px|Figure 17 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 18 ]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 19 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 20 imaginary vibration]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 21 ]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 22 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 23 ]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 24 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 25 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|Figure 26 product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 27 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|Figure 28 product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 29 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|Figure 30 product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 31 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|Figure 32 product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 33 imaginary vibration]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 34 ]]

[[File:IRCDATA.PNG|thumb|right|350px|Figure 35 ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|Figure 36 ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|Figure 37 ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 38 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 39 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 40 ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 41 ]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 42 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 43 HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 44 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 45 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 46 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 47 ]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 48 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 49 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 50 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 50 ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 51 lowest vibration]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 52 imaginary vibration]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 53 ]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|Figure 54 ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|Figure 55 ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 56 ]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 57 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 58 ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 59 ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 60 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 61 lowest vibration ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 62 imaginary vibration ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 63 ]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|Figure 64 ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|Figure 65 ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 66 ]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 67 ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 68 HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 69 LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 70 lowest vibration ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 71 imaginary vibration ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 72 ]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|Figure 73 ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|Figure 74 ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained due to the difference in the magnitude of the secondary interaction between carbon on the diene and the carbonyl carbon. For the molecular interaction, there are two fundamental interaction, primary, secondary. Primary interaction represents the molecular orbital interaction in which bond is forming or breaking, in other words active site of the reaction. Secondary interaction represents the molecular interaction between the atoms which are noe involved in the bond forming of breaking.In this case, compared to exo transition state, the carbon atoms on diene are closer to the carbonyl carbon in endo, which means a stronger secondary interaction and better orbital overlap . Therefore, the endo transition state is more satble.

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

Rep:Mod:angela910118

2013-02-08T16:07:33Z

Mc1210: /* Exo transition state */

Rep:Mod:angela910118

2013-02-08T16:05:52Z

Mc1210: /* The regioselectivity of the Diels Alder Reaction */

Rep:Mod:angela910118

2013-02-08T16:04:05Z

Mc1210: /* Cope Rearrangement */

Rep:Mod:angela910118

2013-02-08T15:49:51Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained due to the difference in the magnitude of the secondary interaction between carbon on the diene and the carbonyl carbon. For the molecular interaction, there are two fundamental interaction, primary, secondary. Primary interaction represents the molecular orbital interaction in which bond is forming or breaking, in other words active site of the reaction. Secondary interaction represents the molecular interaction between the atoms which are noe involved in the bond forming of breaking.In this case, compared to exo transition state, the carbon atoms on diene are closer to the carbonyl carbon in endo, which means a stronger secondary interaction and better orbital overlap . Therefore, the endo transition state is more satble.

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

Rep:Mod:angela910118

2013-02-08T15:48:16Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained due to the difference in the magnitude of the secondary interaction between carbon on the diene and the carbonyl carbon. For the molecular interaction, there are two fundamental interaction, primary, secondary. Primary interaction represents the molecular orbital interaction in which bond is forming or breaking, in other words active site of the reaction. Secondary interaction represents the molecular interaction between the atoms which are noe involved in the bond forming of breaking.In this case, compared to exo transition state, the carbon atoms on diene are closer to the carbonyl carbon in endo, which means a stronger secondary interaction. Therefore, the endo transition state is more satble.

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

Rep:Mod:angela910118

2013-02-08T15:47:08Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained due to the difference in the magnitude of the secondary interaction between carbon on the diene and the carbonyl carbon. For the molecular interaction, there are two fundamental interaction, primary, secondary. Primary interaction represents the molecular orbital interaction in which bond is forming or breaking, in other words active site of the reaction. Secondary interaction represents the molecular interaction between the atoms which are noe involved in the bond forming of breaking.In this case, compared to exo transition state, the carbon atoms on diene are closer to the carbonyl carbon in endo, which means a stronger secondary interaction. Therefore, the endo transition state is more satble.

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

Rep:Mod:angela910118

2013-02-08T15:46:46Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained due to the difference in the magnitude of the secondary interaction between carbon on the diene and the carbonyl carbon. For the molecular interaction, there are two fundamental interaction, primary, secondary. Primary interaction represents the molecular orbital interaction in which bond is forming or breaking, in other words active site of the reaction. Secondary interaction represents the molecular interaction between the atoms which are noe involved in the bond forming of breaking.In this case, compared to exo transition state, the carbon atoms on diene are closer to the carbonyl carbon in endo, which means a stronger secondary interaction. Therefore, the endo transition state is more satble.

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

Rep:Mod:angela910118

2013-02-08T15:28:25Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained because the interaction between hydrogen on the diene and the carbonyl carbon

[[File:Endo angle.PNG|thumb|left|350px|Figure 1 Endo molecule]]

[[File:Exo angel.PNG|thumb|right|350px|Figure 2 Exo molecule ]]

For both transition states, there is only one imaginary vibration occurs and both vibration is perpendicular to the node planer. This vibration is related to the formation of the new carbon carbon sigma bond.

File:Endo angle.PNG

2013-02-08T15:26:55Z

Mc1210:

File:Exo angel.PNG

2013-02-08T15:26:11Z

Mc1210:

Rep:Mod:angela910118

2013-02-08T15:18:31Z

Mc1210: /* Further discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained because

Rep:Mod:angela910118

2013-02-08T15:17:50Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

Compared to endo transition state, exo is higher in energy(exo -0.05041982 a.u. endo -0.05150466). The exo transition state is more strained because

===Further discussion===

Rep:Mod:angela910118

2013-02-08T15:06:02Z

Mc1210: /* The Diels Alder Cycloaddition */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T15:03:08Z

Mc1210: /* Endo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T15:02:10Z

Mc1210: /* Exo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T15:01:33Z

Mc1210: /* Exo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T15:00:35Z

Mc1210: /* Exo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:59:37Z

Mc1210: /* Exo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:58:57Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

The RMS gradient along the IRC calculation is close to zero, which indicates that the local minimum is located.

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:47:24Z

Mc1210: /* Endo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:46:31Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:44:04Z

Mc1210: /* Endo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[File:Lumohomo.png|thumb|center|350px|Figure 1 reactant]]

In order to interact, two molecular orbitals should have the same symmetry and similar energy level.So the transition state HOMO and LUMO is the results of the butadiene and ethylene HOMO LUMO interation.

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:41:19Z

Mc1210: /* Endo transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[File:Lumohomo.png|thumb|center|250px|Figure 1 reactant]]

====Discussion====

===Further discussion===

File:Lumohomo.png

2013-02-08T14:41:04Z

Mc1210:

Rep:Mod:angela910118

2013-02-08T14:29:03Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:28:32Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

The imaginary frequency is -956.09 cm-1.The vibration is perpendicular to the node planer and it is related to the formation of the new carbon bond. So it is bonds synchronous

The lowest frequency is 147.33 cm-1.The vibration is along the node planer and it is not related to the formation of the new carbon bond. So it is bonds asynchronous.

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:17:46Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å. Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å. It indicates the the carbon carbon bond is not fully bonded and it is still in transition state.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:13:44Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30 Å

Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:13:17Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

The partially formed canrbon carbon bond is 2.30

Typical sp3 carbon bond is 1.54 Å. Typical sp2 carbon bond is 1.46 Å. The van der Waals radius of the carbon is 1.7 Å.

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:05:40Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:04:50Z

Mc1210: /* Optimisation the transition state */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:TS HOMO.PNG|thumb|left|350px|Figure 9 HOMO ]]

[[File:TS LUMO.PNG|thumb|right|350px|Figure 10 LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

File:TS LUMO.PNG

2013-02-08T14:04:30Z

Mc1210:

Rep:Mod:angela910118

2013-02-08T14:03:04Z

Mc1210: /* Optimisation the reactant */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is symmetric.LUMO is anti-symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T14:01:12Z

Mc1210: /* Optimisation the reactant */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Ethylenehomo.PNG|thumb|left|250px|Figure 9 HOMO ]]

[[File:Ethylenelumo.PNG|thumb|right|250px|Figure 10 LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

File:TS HOMO.PNG

2013-02-08T14:00:49Z

Mc1210:

File:Ethylenelumo.PNG

2013-02-08T13:59:56Z

Mc1210: uploaded a new version of "File:Ethylenelumo.PNG"

File:Ethylenehomo.PNG

2013-02-08T13:58:53Z

Mc1210: uploaded a new version of "File:Ethylenehomo.PNG"

Rep:Mod:angela910118

2013-02-08T13:53:56Z

Mc1210: /* Optimisation the reactant */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:52:59Z

Mc1210: /* Optimisation the reactant */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric
'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

HOMO is anti-symmetric.LUMO is symmetric

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:50:12Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

1 a.u. = 627.509 kcal/mol

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:49:48Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || 42
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:49:05Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 ||
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || -231.539539
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:48:20Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 || -234.611710
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| 34.1 || -231.539539
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:47:13Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 3: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 || -234.611710
|}

{| class="wikitable" border="1"
|+ '''Table 4: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| -231.539540 || -231.539539
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:46:46Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.469203
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.461856
|-
| H=E+RT || -234.408064 || -234.395063 ||
|-
| G=H-TS || -234.443814 || -234.431753 ||
|-
| Electronic energy || -234.55698303 || -234.54309307 || -234.611710
|}

{| class="wikitable" border="1"
|+ '''Table 2: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| -231.539540 || -231.539539
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===

Rep:Mod:angela910118

2013-02-08T13:36:05Z

Mc1210: /* Discussion */

=Introduction=

==Major purpose of this experiment==
The molecular mechanics method is good for finding the structure of the product but not suitable for analysis the structure of the transition state, in other words it is not helpful for describing the formation or cleavage of the bonds.By using molecular orbital-based methods, the potential surface of the reaction is analysed in order to determined the location and structure of the transition state. Information like activation energy, the reaction energy path can be calculated out.In this case, we focus on Diels Alder cycloaddition reactions as well as cope rearrangement

==What programme is used==

GaussView 5.0.9 is used here.

=Cope Rearrangement=

In this section, different type of geometries of1,5-hexadiene is analysed below. In total, there are 10 type of structures but we will only discuss 4 of them.

==Optimizing the Reactants and Products==

===Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22978 | click here]]

[[File:15hexadiene opt symmetrize.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Chefile datasummary 15hexadiene.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001291 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-2.285645D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is Ci

===Optimizing gauche (2) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22979 | click here]]

[[File:Optimisationstructure.PNG|thumb|left|250px|Figure 3 gauche(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata.PNG|thumb|right|250px|Figure 4 a table of data summary of gauche(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000418 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-2.077361D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing anti (1) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22990 | click here]]

[[File:Anti1 optimisation.PNG|thumb|left|250px|Figure 5 anti(1) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti1datasummary.PNG|thumb|right|250px|Figure 6 a table of data summary of anti(1) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001583 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090750D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2

===Optimizing gauche (3) 1,5-hexadiene===

Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22991 | click here]]

[[File:Gauche3 optimisation.PNG|thumb|left|250px|Figure 7 gauche(3) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Summarydata 3.PNG|thumb|right|250px|Figure 8 a table of data summary of gauche(3) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000033 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001259 0.001800 YES
RMS Displacement 0.000424 0.001200 YES
Predicted change in Energy=-1.726756D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

===Comparison bewtween anti and gauche 1,5-hexadiene===

All four 1,5 hexadiene calcualtion is carried out under this condition:
Job type: Optimisation Method: Hartree Fock Basis set: 3-21G

{| class="wikitable" border="1" align="center"
|+ Table:1 data summary of the optimization of 1,5-hexadiene
! Molecule Conformation !!Final Energy/ a.u.!! RMS Gradient Norm /a.u.!! Dipole moment /Debye!!Point Group
|-
| '''anti(2)'''||-231.69254||0.00001339||0.0003||Ci
|-
|'''anti(1)'''||-231.69260||0.00000456||0.2021||C2
|-
|'''gauche(2)'''||-231.69167||0.00001824||0.3805||C2
|-
|'''gauche(3)'''||-231.69266|| 0.00001095 ||0.3407 ||C1
|}

[[File:Antigauche.png|thumb|center|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

According to the table and graph above,the final energy,electronic energy of two anti conformations are more negative than that of two gauche geometry. As the two substituents on the gauche is next to each other(the angle between two subsitituents is 60),the steric effect makes the structure to be more unstable, which gauche geometry results in having higher final energy.However, the two substituents are 180 degree away from each other.According to the Appendix 1, the relative energy of gauche 3 is 0 kcal/mol while that of gauche 2 is 0.62 kcal/mol. The difference of relative energy between two anti geometries is small,anti(2) 0.4 kcal/mol, anti (1) 0.8 kcal/mol.

===Further Optimizing anti (2) 1,5-hexadiene===

Job type: Optimisation Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22992 | click here]]

[[File:Anti12 optimisation.PNG|thumb|left|250px|Figure 9 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Anti12 optimisationdatasummary.PNG|thumb|right|250px|Figure 10 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000581 0.001800 YES
RMS Displacement 0.000228 0.001200 YES
Predicted change in Energy=-8.253337D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure after symmetric is Ci,which is exactly the same as the point group gained by calculation using basis set 3-21G.In other words, the structure of the moleucle dose not have sinificant change after being optimized at two different level.

For method of 3-21G, the final energy of the molecule is -231.69 a.u.For method of 6-31G(d), the final energy of the molecule is -231.56 a.u. which is relatively lower.

However, although the point group of the two optimized molecules dose not change, the individual bond lengths have been changed. The carbon carbon double bonds are expected to shorter in the calculation using basis set 3-21G (3-21G, 1.316 6-31G(d),1.338)and the carbon single bonds are also expected to be shorter in the calculation using basis set 3-21G (3-21G, 1.553 6-31G(d), 1.555). However the dihedral angles for both optimizations are about the same, around 180 degree.

===Frequncy anaylsis anti (2) 1,5-hexadiene===
Two different basis sets are used for frequency calculations.

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22994 | click here]]

[[File:Frequncydatasummary anti2.JPG|thumb|center|250px|Figure 11 a table of data summary of anti(2) 1,5 hexadiene frequency calculation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001680 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-1.964588D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

The D space calculation is provided:[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/22993 | click here]]

[[File:Frequncydatasummary.JPG|thumb|center|250px|Figure 12 a table of data summary of anti(2) 1,5 hexadiene frequency calculation]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000107 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000529 0.001800 YES
RMS Displacement 0.000238 0.001200 YES
Predicted change in Energy=-8.713057D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Thermochemistry'''

Four quantities has been recorded in the log output file,which have 4 different meanings in turns of energy:

'''(1)'''Sum of electronic and zero-point Energies represents the sum of the potential energy at 0 K and zero potential energy.E=Eelec+ZPE

'''(2)'''Sum of electronic and thermal Energies represents energy at 298.15 K and 1 atm of
pressure which includes the contribution of translation, vibration, rotation.E=E+Evib+Erot+Etrans

'''(3)'''Sum of electronic and thermal Enthalpies represents the energy associated with RT. H=E+RT

'''(4)'''Sum of electronic and thermal Free Energies represents the entropic contribution of free energy. G=H-TS

Data gained from calculation using basis set 3-21G
<pre>
Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570914
</pre>

Data gained from calculation using basis set 6-31G(d)
<pre>
Sum of electronic and zero-point Energies= -234.416252
Sum of electronic and thermal Energies= -234.408952
Sum of electronic and thermal Enthalpies= -234.408008
Sum of electronic and thermal Free Energies= -234.447896
</pre>

Comparison between experimental data and the literature data

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data comparison for anti(2)1,5-hexadiene'''
!Energy !! Data gained from calcualtion using 3-21G/ a.u. !! literature value for calcualtion using 3-21G/ a.u. !! Data gained from calcualtion using 6-31G(d)/ a.u. !! literature value for calcualtion using 6-31G(d)/ a.u.
|-
| E=Eelec+ZPE || -231.539540 || -231.539539 || -234.416252 ||-234.469203
|-
| E=E+Evib+Erot+Etrans || -231.532566 || -231.532566 || -234.408952 ||-234.461856
|-
| H=E+RT || -231.531622 || || -234.408008 ||
|-
| G=H-TS || -231.570914 || || -234.447896 ||
|-
| Electronic energy || -231.69253528 || -231.692535 || -234.55969668 || -234.611710
|}

All the experiment data is almost the same as the literature value. This indicateds the calculation preformed is correct.

'''The predicted IR spectrum'''

'''First calcualtion:'''

Job type: Frequency Method: Hartree Fock Basis set: 3-21G

[[File:IRforanti.PNG|thumb|center|500px|Figure 13 IR spectrum]]

'''Second calcualtion:'''

Job type: Frequency Method: DFT B3LYP Basis set: 6-31G(d)

[[File:IRforanti2 631g.PNG|thumb|center|500px|Figure 14 IR spectrum]]

==Optimizing Chair and Boat Transition Structures==

As the chair and boat transition structures are both made from allyl fragments.In this section, optimisation calculation is carried out for allyl fragments, chair transition, boat transition.Frequency analysis and IRC calculations are also preformed in order to discover the physical properties of the transition states

===Optimizing allyl fragment===

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:CHAIR 1 OPTIMIASATION.LOG‎‎|click here]]

[[File:Ch2chch2structure.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Data.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

===Optimizing chair transition state===

There are two ways to optimize this transition state.The easiest way is using hessian method to calculate.In order to do so, the estimated transition structure has to be reasonable.Otherwise,a better calculation is preformed by freezing the reaction coordinate.Two different ways of calculation is preformed below.

==== Optimization by hessian method====

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:D2H OPTI FRE 2.LOG‎‎|click here]]

[[File:D2H OPTI FRE 1.JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Datasummary D2H OPTI FRE 1opti 1.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000385 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.460758D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495206
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -818cm-1

<pre>
Low frequencies --- -817.9850 -0.9874 -0.0007 -0.0006 0.0006 1.5634
Low frequencies --- 2.9830 209.5556 396.0027
</pre>

[[File:Imarginaryfre 818.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

==== Optimization by frozen coordinate method====

'''Step One'''

Before preforming the optimization calculation,freeze two pairs of carbon atoms which will form new sigma bond though the the Redundant Coord Editor in the edit menu.

Job type: Optimization,optimize to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

The distance of two pairs of carbon which will form two carbon carbon single bonds is set to 2.2 Å that is a bond length of a carbon carbon single bond.

The log file of optimisation:[[media:FREEZE OPTIMISATION.LOG‎‎|click here]]

[[File:Freeze optimisation(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Freeze optimisation datasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000891 0.001800 YES
RMS Displacement 0.000124 0.001200 YES
Predicted change in Energy=-2.748211D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

'''Step Two'''

Before preforming the optimization calculation,change "Bond" and "Freeze Coordinate" to "Bond" and "Derivative" in the Redundant Coord Editor of the edit menu.

Job type: Opt+Fre optimization to a TS(Berny) Method: Hartree Fock Basis set: 3-21G Additional keyword is Opt=NoEigen

Because of step one. the breaking or forming carbon carbon sigma bond is fixed to 2.2 Å.

The log file of optimization:[[media:FREEZE OPTIMISATION PART D.LOG‎‎|click here]]

[[File:Capture(1).JPG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

[[File:Freeze optimisation part d datasummary.JPG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001302 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.296662D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.495207
</pre>

====Comparison of two optimization method====

From the two optimized transition structure, the point groups of two optimized transition states are the same, C1. Moreover, the distances between two allyl fragments are the same,2.02 Å.The final energy of the transition state is lower in hessian method,-231.61932246 a.u.(final energy of frozen coordinate method is -231.61540391 a.u. ).

===Optimizing boat transition state===

Compared to the method used to calculate the chair transition state, the method used for boat transition state is QST2. The reason for using QST2 method is that is possibly to specify the reactant and product of the reaction and is possible to discover the transition state of the reaction.In order to carry out OST2 calculation, the label of the atoms of reactant molecule is changed manually, which therefore it correspond to the label of the atoms of product molecule.

====Failed Calculation====

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation product.PNG|thumb|right|250px|product ]]

[[File:Failed boat optimisation.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Failed optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.001475 0.001800 YES
RMS Displacement 0.000382 0.001200 YES
Predicted change in Energy=-2.238101D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2H

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.466701
Sum of electronic and thermal Energies= -231.461341
Sum of electronic and thermal Enthalpies= -231.460397
Sum of electronic and thermal Free Energies= -231.494552
</pre>

As you can see above, the optimized structure is similar to a chair transition state. What is expected is a boat transition state. So the calculation is failed.

==== Successful Calculation====

In order to obtain the correct transition state, a few changes in the input file of the calculation is made. The dihedral angle is changed to 0 degree and the C-C-C bond is altered to 100 degree.

Job type: Opt+Freq, optimize to TS (QST2) Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:BOAT OPTIMISATION.LOG‎‎|click here]]

[[File:Boat optimisation correct reactant.PNG|thumb|left|250px|Figure 1 reactant]]

[[File:Boat optimisation correct product.PNG|thumb|right|250px|product ]]

[[File:Correct optimisation.JPG|thumb|left|250px|Figure 1 reactant]]

[[File:Correct optimisationdata.JPG|thumb|right|250px|product ]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
Predicted change in Energy=-7.023936D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C2V

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -231.450931
Sum of electronic and thermal Energies= -231.445302
Sum of electronic and thermal Enthalpies= -231.444358
Sum of electronic and thermal Free Energies= -231.479776
</pre>

According to the frequency calculation, the data gained indicates there is only one imaginary frequency which is -839cm-1

<pre>
Low frequencies --- -839.3504 -5.5667 -0.0016 -0.0013 -0.0010 2.3760
Low frequencies --- 4.3926 155.4092 381.8052
</pre>

[[File:Correct imaginaryfre.gif|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Intrinsic Reaction Coordinate calculation of chair transition state===

It is impossible for us to predict which conformer will be formed from the transition state though the reaction paths. Intrinsic Reaction Coordinate calculation helps us to follow the minimum energy reaction path way from the transition state to a local potential minimum on the surface.

====First Intrinsic Reaction Coordinate calculation====

Job type: IRC, forward direction, force constant once, calculate always, the number of points along the IRC= 50 Method: Hartree Fock Basis set: 3-21G

[[File:CHAIRTRANSITIONSTATE.gif|thumb|left|350px|Figure 1 reactant]]

[[File:IRCDATA.PNG|thumb|right|350px|product ]]

[[File:TOTAL ENERGY ALONG IRC.PNG|thumb|left|350px|product ]]

[[File:RMSGRADIENT ALONG IRC.PNG|thumb|right|350px|product ]]

As you can see from the graph above, the RMS gradient is almost zero. It incicates that the calculation has almost find the local minimun of the potential surface.

====Optimisation after Intrinsic Reaction Coordinate calculation====

Sometimes the IRC calculation will not reach a minimum geometry. Another optimization is preformed for the last point of the IRC calculation. In this case,although the data of IRC indicates the minimum geometry is almost reached, the optimization is still preformed to double check whether the data gained above is correct or not.

Job type: Optimization Method: Hartree Fock Basis set: 3-21G

The log file of optimization:[[media:IRC OPT.LOG‎‎|click here]]

[[File:Irc opt datasummary.PNG|thumb|center|350px|Figure 1 reactant]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000299 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.412878D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

As you can see the final energy of the optimization is slight lower than the energy calculated by IRC method.It proves that the IRC calculation reaches the minimum geometry.

===Activation energy analysis===

In this section, both chair and boat transition state is optimized at a more accurate level,B3LYP/6-31G (d) level. The following frequency analysis helps us to obtain the thermochemistry data in order to calculate the activation energy of both transition states

====Reoptimizing chair transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:CHAIR631OPTFRE.LOG‎‎|click here]]

[[File:ChairTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.291256D-09
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

The thermochemistry of the chair transition state

<pre>
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
</pre>

==== Reoptimizing boat transition state====

Job type: Opt+Fre optimization to a TS(Berny) Method: B3LYP Basis set: 6-31G(d) Additional keyword is Opt=NoEigen

The log file of optimization:[[media:BOAT OPTIMISATION 631G.LOG‎‎|click here]]

[[File:BoatTS631datasummary.PNG|thumb|center|250px|Figure 1 anti(2) 1,5 hexadiene after optimization and symmetrization]]

The output file confirm the calculation is converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.210786D-11
Optimization completed.
-- Stationary point found.
</pre>

The point group of this structure is C1

The thermochemistry of the boat transition state

<pre>
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431753
</pre>

====Discussion====

{| class="wikitable" border="1"
|+ '''Table 2: Thermochemistry data of two transition states'''
!Energy !! Chair conformation !! Boat conformation !! anti(2) 1,5-hexadiene
|-
| E=Eelec+ZPE || -234.414929 || -234.402342 || -234.416252
|-
| E=E+Evib+Erot+Etrans || -234.409008 || -234.396008 || -234.408952
|-
| H=E+RT || -234.408064 || -234.395063 || -234.408008
|-
| G=H-TS || -234.443814 || -234.431753 || -234.447896
|-
| Electronic energy || -234.55698303 || -234.54309307 || -234.55969668
|}

{| class="wikitable" border="1"
|+ '''Table 2: Activation energy'''
!Activation energy !! Chair conformation !! Boat conformation
|-
|Activation energy at 0 K experiment data|| -231.539540 || -231.539539
|-
|Activation energy at 0 K literature data|| 33.5 ± 0.5 || 44.7 ± 2.0
|}

[[discussion]]

==The Diels Alder Cycloaddition==
The Diels Alder reaction is one type of the pericyclic reactions. The most important feature is that the pi bonds of the dieneophile and diene will overlap with each other to form a new sigma bond.In terms of molecular orbitals, this new sigma bond will only formed under these condition:the HOMO of one reactant interacts with the other reactant's LUMO; the overlap between two reactant orbital is significant enough;the overlap orbitals are having the same symmetry. In this case, the HOMO and LUMO of the butadiene are both symmetric and the HOMO and LUMO of ethyleneare both anti symmetric. The new formed sigma bond therefore is anti symmetric.

[[File:INTRODUCTION.png|thumb|center|250px|Figure 14 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

===Optimisation the reactant===

Butadiene and ethylene are both optimised. Each HOMO and LUMO are predicted graphically.

'''Butadiene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:BUTANDIENE OPTI.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.212207D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

'''Ethylene'''

Job type: Optimisation Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ETHYLENE.LOG‎‎|click here]]

[[File:Butadiene.PNG|thumb|left|250px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Butadienedatasummary.PNG|thumb|right|250px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000162 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000414 0.001800 YES
RMS Displacement 0.000220 0.001200 YES
Predicted change in Energy=-3.787280D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C2V

[[File:Homo.PNG|thumb|left|250px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|250px|Figure 10 butadiene LUMO ]]

[[ labeling each as symmetric or anti symmetric]]

===Optimisation the transition state===

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:TRANSITIONSTATE OPT.LOG‎‎|click here]]

[[File:Ts.JPG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:TS OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000741 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-1.689969D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IR SPECTRUM OF THE TS.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:TS LOW.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:TS IMAG.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:IRC CALCUALTION.LOG‎‎|click here]]

[[File:CHAIRTRANSITIONSTATE.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:Ircfortotalenergy.PNG|thumb|left|350px|product ]]

[[File:Ircforrmsgradient.PNG|thumb|right|350px|product ]]

[[discussion]]

===The regioselectivity of the Diels Alder Reaction===

====Exo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:Entering Link 1.docx‎‎|click here]] as the log file is too big to upload, it is saved as a work file.

[[File:TS afteropt fre.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:EXO OPT DATASUMMARY.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000755 0.001800 YES
RMS Displacement 0.000198 0.001200 YES
Predicted change in Energy=-3.582496D-08
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Exo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Exo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:IRFOREXO.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:EXO lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:EXO imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:EXO IRC.LOG|click here]]

[[File:Exo trasitio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:ExoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:ExoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Endo transition state====

'''Optimisation and frequncy anaylsis'''

Job type: Opt+Freq Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO OPT FRE.LOG‎‎|click here]]

[[File:Endo opt.PNG|thumb|left|350px|Figure 1 anti(2) 1,5 hexadiene after optimisation and symmetrization]]

[[File:Endodatasummary.PNG|thumb|right|350px|Figure 2 a table of data summary of anti(2) 1,5 hexadiene optimisation ]]

The output file confirm the calculation is converged.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000171 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.001704 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-1.429627D-07
Optimization completed.
-- Stationary point found.
</pre>

The point group of this stucture after symmetrize is C1

'''HOMO and LUMO'''

[[File:Endo homo.PNG|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo lumo.PNG|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''Predicted IR spectrum'''

[[File:EndoIR.PNG|thumb|center|500px|Figure 9 butadiene HOMO ]]

'''Imaginary frequency and Lowest frequency'''

[[File:Endo lowestfre.gif|thumb|left|350px|Figure 9 butadiene HOMO ]]

[[File:Endo imaginaryfre.gif|thumb|right|350px|Figure 10 butadiene LUMO ]]

'''IRC anaylsis'''

Job type: IRC, both directions, force constant once, calculate always, the number of points along the IRC= 50 Method: semi-empirical Basis set: AM1

The log file of optimisation:[[media:ENDO-IRC.LOG‎‎|click here]]

[[File:Endotransistio.gif|thumb|center|250px|Figure 1 reactant]]

'''Gradient and energy change along the IRC claculation'''

[[File:EndoIRC TOTALENERGY.PNG|thumb|left|350px|product ]]

[[File:EndoIRC RMSGRADIENT.PNG|thumb|right|350px|product ]]

[[discussion]]

====Discussion====

===Further discussion===