ChemWiki - User contributions [en]

Rep:Mod:yixingphysical

2013-12-06T16:21:41Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature<ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

''' 1.Geometry Comparison'''

[[Image:44444444444.PNG]]

{| class="wikitable"
|-
| Terms|| Result from AM1 Optimization || Result from 6-31G*Optimization || Literature Value<ref> Goldstein, E.; Beno, B.; Houk, K. N.; ''J. Am. Chem. Soc.,'' 1996, '''''118,''''' 6036-6043. DOI:10.1021/ja9601494</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> and C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.3820 || 1.3820 || 1.383
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.3975 || 1.4072 || 1.407
|-
| C<sub>5</sub>-C<sub>6</sub> Bond Length/Å || 1.3830 || 1.3830 || 1.386
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Interfragmental Distance/ Å || 2.1194 || 2.2722 || 2.273
|}

The 6-31G* method provided a more accurate structure since all values were closer to literature than the AM1 semi-empirical MO method.

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

==Reference==
<references/>

File:44444444444.PNG

2013-12-06T16:20:52Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T16:11:17Z

Dd611: /* Diels Alder Cycloaddition */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature<ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

==Reference==
<references/>

Rep:Mod:yixingphysical

2013-12-06T16:10:58Z

Dd611: /* Reference */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature<ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

Rep:Mod:yixingphysical

2013-12-06T16:06:54Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature<ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Reference==
<references/>

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

Rep:Mod:yixingphysical

2013-12-06T16:04:13Z

Dd611: /* Cope Rearrangement */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Reference==
<references/>

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

Rep:Mod:yixingphysical

2013-12-06T16:00:43Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''1.Thermochemistry Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

'''2.Geometry Comparison'''

[[Image:Final_last_2nd.PNG]]

{| class="wikitable" border="1"
| Parameter || HF/3-21G || B3LYP/6-31G* || Literature Value<ref>Michael J. S. Dewar , George P. Ford , Michael L. McKee , Henry S. Rzepa , Leslie E. Wade. ''J. Am. Chem. Soc.'', 1977, '''''99 (15),'''''5069–5073</ref>
|-
| C<sub>1</sub>-C<sub>2</sub> Distance/ Å || 2.3736 || 2.3736 || 1.599
|-
| C<sub>4</sub>-C<sub>5</sub> Distance/ Å || 2.4452 || 2.4452 || 1.899
|-
| C<sub>2</sub>-C<sub>3</sub> and C<sub>5</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.474
|-
| C<sub>3</sub>-C<sub>4</sub> and C<sub>1</sub>-C<sub>6</sub> Bond Length/ Å || 1.4075 || 1.4075 || 1.382
|-
| C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub> Bond Angle || 119.7048<sup>o</sup> || 112.4944<sup>o</sup> || 113.4<sup>o</sup>
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle || 107.4615<sup>o</sup> || 103.6352<sup>o</sup> || 106.4<sup>o</sup>
|-
| Dihedral Angle || 64.0448<sup>o</sup> || 65.1817<sup>o</sup> || None
|}

As can be seen from the table that no accurate optimization result was obtained comparing to the literature. This might be due to the inter-fragmental distance of 2.2Å which was set manually.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

File:Final last 2nd.PNG

2013-12-06T15:55:27Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T15:51:51Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

The first approach of the chair TS was chosen to undergo the optimization using the higher basis level and the results were listed below.

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

Comparing to the values on the script, all the energies matched up to an acceptable extent which indicates that the optimization was successful. It can be seen that the higher basis method gave a lower magnitude of the energies than the HF/3-21G basis; thus higher basis would provide more stable structure.

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

Rep:Mod:yixingphysical

2013-12-06T15:44:35Z

Dd611: /* Result and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

The energy difference between HOMO and LUMO in exo adduct is 0.30230 a.u. (189.70 kcal/mol)

The energy difference between HOMO and LUMO in endo adduct is 0.30937 a.u. (197.13 kcal/mol)

Exo adduct had quite slightly lower energy difference than endo adduct. HOMO of exo lies lower in energy than endo while LUMO of exo lies higher than endo does.

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap which states that the interaction between pi orbitals were not involved in the bond-forming reaction. Endo adduct had significant secondary orbital overlap whereas exo adduct did not. This was due to the opposite orientation between =CH-CH= and -(C=O)-(C=O)- in exo adduct. The Secondary Orbital Overlap effect overcame the steric hindrance and the endo adduct was the predominate product in this reaction.

Rep:Mod:yixingphysical

2013-12-06T15:32:33Z

Dd611: /* Result and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''1.HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

'''2.Geometry Comparison'''

[[Image:GEOMETRY COMPARISION.PNG]]

{| class="wikitable" border="1"
! Terms!! Optimized Exo TS !! Optimized Endo TS
|-
| C<sub>5</sub>=C<sub>6</sub> Bond Length/Å || 1.3968 || 1.3972
|-
| C<sub>7</sub>-C<sub>8</sub> Bond Length/ Å || 1.4101 || 1.4085
|-
| C<sub>1</sub>-C<sub>6</sub> and C<sub>4</sub>-C<sub>5</sub> Bond Length/ Å || 1.3944 || 1.3930
|-
| C<sub>7</sub>-C<sub>10</sub> and C<sub>8</sub>-C<sub>9</sub> Bond Length/ Å || 1.4882 || 1.4892
|-
| C<sub>1</sub>-C<sub>7</sub> and C<sub>4</sub>-C<sub>8</sub> Interfragmental Distance/ Å || 2.1704 || 2.1623
|}

Conclusion:

1. There was not a quite large difference in bond length between endo and exo TS.

2. Comparing to typical C-C or C=C bond length, neither of them was formed.

3. The inter-fragmental distance between C1 and C7 as well as C4 and C8 were close to 2.2Å.

'''3. Thermochemistry Comparison'''

{| class="wikitable" border="1"
|The total electronic energy of exo adduct|| -0.05041985 a.u.
|-
|The total electronic energy of endo adduct || -0.05150478 a.u.
|}

It can be seen that there was not quite a large energy difference between the exo and endo adducts; hence, it is possible that the reaction would proceed via either of the transition states.

[[Image:ENERYG COMPARSION.PNG||400px]]

Secondary orbital overlap:

As can be seen from the mechanism above, the endo adduct was more sterically hindered and less stable thermodynamically, but it was the main product experimentally. This could be explained by secondary orbital overlap. In the alkene fragment, the C=O group was electron withdrawing; therefore, there was a better overlap between the LUMO of hexadiene with the pi-orbital of C=O group. The electron-withdrawing group added more stability so the endo adduct would actually have lower energy.

File:ENERYG COMPARSION.PNG

2013-12-06T15:25:57Z

Dd611:

File:GEOMETRY COMPARISION.PNG

2013-12-06T15:11:05Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T15:05:37Z

Dd611: /* Result and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''HOMO LUMO'''

In order to have orbital overlap, the orbitals must have same symmetry and similar energy. There were two overlap interactions: symmetric overlap between HOMO of maleic anhydride and LUMO of hexadiene; and antisymmetric overlap between HOMO of hexadiene and LUMO of maleic anhydride. Details are shown in the below figure.
[[Image:Captu000re.PNG]]

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

File:Captu000re.PNG

2013-12-06T15:00:31Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T14:43:36Z

Dd611: /* Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, there are more molecules which have the enough energy to come over the energy barrier. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''HOMO LUMO'''

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

Rep:Mod:yixingphysical

2013-12-06T14:39:13Z

Dd611: /* Result and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, the activation energy will decrease. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier. Hence, the minimum energy required for the reaction would be lower.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

'''HOMO LUMO'''

HOMO of EXO adduct
[[Image:EXO HOMO.PNG||200px]]
[[Image:EXO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of EXO adduct
[[Image:EXO LUMO.PNG||200px]]
[[Image:EXO LUMO 2.PNG||200px]]
Anti-symmetric

HOMO of ENDO adduct
[[Image:ENDO HOMO.PNG||200px]]
[[Image:ENDO HOMO 2.PNG||200px]]
Anti-symmetric

LUMO of ENDO adduct
[[Image:ENDO LUMO.PNG||200px]]
[[Image:ENDO LUMO 2.PNG||200px]]
Anti-symmetric

File:ENDO LUMO 2.PNG

2013-12-06T14:35:13Z

Dd611:

File:ENDO LUMO.PNG

2013-12-06T14:35:13Z

Dd611: uploaded a new version of "File:ENDO LUMO.PNG"

File:ENDO HOMO 2.PNG

2013-12-06T14:35:12Z

Dd611:

File:ENDO HOMO.PNG

2013-12-06T14:35:12Z

Dd611: uploaded a new version of "File:ENDO HOMO.PNG"

File:EXO LUMO 2.PNG

2013-12-06T14:35:12Z

Dd611:

File:EXO LUMO.PNG

2013-12-06T14:35:11Z

Dd611: uploaded a new version of "File:EXO LUMO.PNG"

File:EXO HOMO 2.PNG

2013-12-06T14:35:11Z

Dd611:

File:EXO HOMO.PNG

2013-12-06T14:35:10Z

Dd611: uploaded a new version of "File:EXO HOMO.PNG"

Rep:Mod:yixingphysical

2013-12-06T14:00:52Z

Dd611: /* Optimization of Exo Product */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, the activation energy will decrease. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier. Hence, the minimum energy required for the reaction would be lower.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

[[Image:EXO ADDUCT.PNG]]

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T13:58:17Z

Dd611: /* Optimization of Endo Product */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, the activation energy will decrease. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier. Hence, the minimum energy required for the reaction would be lower.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====

[[Image:ENDO ADDUCT.PNG]]

'''1.Optimized Endo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO_TS_1st_tttrrryyy.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05150478 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -806.47 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000999 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-2.291370D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -806.47 cm<sup>-1</sup>.

[[File:80647.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 62.51 cm<sup>-1</sup>

[[File:6057.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:ENDO TS 1ST TTTRRRYYY.LOG|here]]

====Result and Discussion====

File:6057.gif

2013-12-06T13:57:37Z

Dd611:

File:EXO ADDUCT.PNG

2013-12-06T13:52:11Z

Dd611:

File:ENDO ADDUCT.PNG

2013-12-06T13:52:10Z

Dd611:

File:ENDO TS 1ST TTTRRRYYY.LOG

2013-12-06T13:48:00Z

Dd611:

File:ENDO TS 1st tttrrryyy.mol

2013-12-06T13:47:59Z

Dd611:

File:80647.gif

2013-12-06T13:47:59Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T13:36:20Z

Dd611: /* Introduction */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, the activation energy will decrease. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier. Hence, the minimum energy required for the reaction would be lower.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===

Diels-Alder cycloaddition has the general mechanism as shown below. In this reaction, two new sigma bonds were formed between two terminal carbons; and also 6 pi-electrons were involved. The process is considered as concerted if the HOMO and LUMO orbitals have the same symmetry and similar energy.

Reaction between ethylene and cis-butadiene and between cyclohexa-1,3-diene and maleic anhydride were studied.

[[Image:Capture222.PNG]]

===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

File:Capture222.PNG

2013-12-06T13:29:27Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T13:24:25Z

Dd611: /* Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===

'''Activation Energy'''

Activation energy is the minimum energy required for an reaction to start. In this experiment, energies of both transition state 'chair' and 'boat' were calculated and listed in the following table.

{| class="wikitable"
|-
| Type of Basis Set || HF/3-21G || HF/3-21G || B3LYP/6-31G* || Experimental|| B3LYP/6-31G*
|-
| Temperature || at 0 K || at 298.15 K || at 0 K || at 0 K|| at 298.15 K
|-
| Ea(Chair) /kcalmol<sup>-1</sup> || 45.71 || 44.70 || 34.09 || 33.5 ± 0.5 || 33.19
|-
| Ea(Boat) /kcalmol<sup>-1</sup> || 55.60|| 54.72 || 42.01 || 44.7 ± 2.0 || 41.32
|}

As can be seen from the table, the results from the B3LYP/6-31G* basis set was much closer to the experimental values; while the HF/3-21 basis set had about 10 kcal/mol energy difference. Thus, it would be better to use the higher basis level.

By comparing the activation energy between temperature 0K and 298.15K, it could be concluded that as temperature increases, the activation energy will decrease. This is because as temperature increases, the average kinetic energy of the molecules are also increased; there will more molecules which have enough energy to jump over the energy barrier. Hence, the minimum energy required for the reaction would be lower.

By comparing the energies between chair and boat transition state, it can be seen that chair transition state requires a lower energy than the boat state; thus, the chair transition state is more thermodynamically stable and would lead to a thermodynamic product. The boat transition state has a higher activation energy so it is kinetically stable.

To conclude, the rearrangement would likely to proceed via the chair transition state at low temperature; and via the boat transition state at high temperature.

==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T11:57:50Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Boat TS ||TS(QST2), HF/3-21G ||-231.60280200 ||-231.450928||-231.445299||-839.94||C<sub>2v</sub>
|-
| ||TS(QST2), B3LYP/6-31G* ||-234.54309304||-234.402339||-234.396005||-530.57 ||C<sub>2v</sub>
|}

All thermochemistry results matched the values on the script as well as the point group; thus, the analysis was successful.

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T11:47:59Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
====Results and Discussion====

'''Results Comparison'''

{| class="wikitable"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Method'''
| align="center" style="background:#f0f0f0;"|'''Electronic Energy (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic Energy and Zero-Point Energies at 0 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Sum of Electronic and Thermal Energies at 298.15 K (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Imaginary Frequency (cm<sup>-1</sup>)'''
| align="center" style="background:#f0f0f0;"|'''Point Group'''
|-
| Chair TS (Normal)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Frozen)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|-
| Chair TS (Derivative)||TS(Berney), HF/3-21G ||-231.61932247 ||-231.466700||-231.461340||-817.93||C<sub>2h</sub>
|-
| ||TS(Berney), B3LYP/6-31G* ||-234.55698303 ||-234.414929||-234.409009||-565.54||C<sub>2h</sub>
|}

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T11:28:43Z

Dd611: /* Third Approach: Optimization to a TS (Berny)with Derivative */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>
===Results and Discussion===

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T11:26:44Z

Dd611: /* Optimization of the 'chair' Transition State */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===

[[Image:11111111111111.PNG]]

1,5-hexadiene undergoes the cope rearrangement via the chair or boat transition state. For chair transition state, the mechanism could be considered as the migration of one allyl fragment.

In order to do this, the CH<sub>2</sub>CHCH<sub>2</sub> fragment was optimized using HF/3-21G method and was used as the basis. Then the transition state was made up with two optimized allyl fragments with a distance of 2.2Å between two terminal carbons. .The chair TS has been investigated using three different approaches: normal optimization, frozen coordinate method and calculation with derivative.

====First Approach: Optimization to a TS (Berny)====

In the first approach of optimization of the transition state, the Berny algorithm was used. This method is the most time-saving but sometimes might lead to inaccurate results.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
The second approach used the frozen coordinates method which set certain atoms frozen; therefore, the bond breaking and bond forming distances were set to be exactly 2.2Å.

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

File:11111111111111.PNG

2013-12-06T11:05:58Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T10:53:49Z

Dd611: /* Optimization of an Allyl Fragment */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

'''1. Optimized Allyl Fragment'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair allyl first.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|Method||HF/3-21G
|-
|Total Energy|| -115.82304010 a.u.
|}

===Optimization of the 'chair' Transition State===
====First Approach: Optimization to a TS (Berny)====

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-06T10:44:11Z

Dd611: /* Results and Discussion */

==Cope Rearrangement==
===Introduction===

1,5-hexadiene could undergo a [3,3]-sigmatropic cope rearrangement as shown below. The mechanism would be via transition state either 'chair' or 'boat'. Enthalpies and energies of both transition states were computed and compared in order to decide the mechanism of the cope rearrangement.

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

{| class="wikitable"
|-
| Type of energy ||Anti-2 B3LYP/631G*|| Gauche-3 B3LYP/631G* || Gauche-4 B3LYP/631G*
|-
| The Sum of Electronic and Zero-Point Energies at 0 K (Hartrees)|| -234.469212 || -234.468693||-234.467784
|-
| The Sum of Electronic and Thermal Energies at 298.15 K (Hartrees) || -234.461856 ||-234.461464||-234.460521
|-
| The Sum of electronic and thermal Enthalpies||-234.460912 ||-234.460520||-234.459577
|-
| The Sum of electronic and thermal Free Energies||-234.500821||-234.500105||-234.498690
|-
| Total Electronic Energy||-231.61170280 ||-231.61132934 ||-231.61048196
|}

Energies and enthalpies of different conformers using B3LYP/631G* were listed in the above table. Although each conformer was investigated using both B3LYP/631G* and HF/321G basis sets, only the results from B3LYP/631G*(the higher level) were discussed here because energies between diffferent method and basis set cannot be compared.

By comparing the energies and enthalpies, it could be concluded that anti-conformer is more stable than the gauche conformers since anti-conformer has relatively lower energy.

'''3.Geometry Comparison'''

The geometry information of the anti-conformer is listed in the following table. Both bond length and bond angles including dihedral angles using two different method and basis set are compared with literature values.

[[Image:1.5 HEXADIENE.PNG]]

{| class="wikitable"
|-
| Terms || HF/3-21G || B3LYP/6-31G* || Literature
|-
| C<sub>1</sub>=C<sub>2</sub> Bond Length/ Å || 1.3162 || 1.3335 || 1.3412
|-
| C<sub>2</sub>-C<sub>3</sub> Bond Length/ Å || 1.5088 || 1.5042 || 1.5077
|-
| C<sub>3</sub>-C<sub>4</sub> Bond Length/ Å || 1.5530 || 1.5481 || 1.5362
|-
| C-H Bond Length/ Å || 1.075 || 1.0997 || 1.1077
|-
| C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub> Bond Angle|| 111.3465<sup>o</sup> || 112.6749<sup>o</sup> || 111.0<sup>o</sup>
|-
| C<sub>1</sub>=C<sub>2</sub>-C<sub>3</sub> Bond Angle || 124.8129<sup>o</sup> || 121.8691<sup>o</sup> || 122.5<sup>o</sup>
|-
| C<sub>2</sub>=C<sub>1</sub>-H Bond Angle || 121.8245<sup>o</sup> || 121.6515<sup>o</sup> || 120.4<sup>o</sup>
|-
| C<sub>3</sub>-C<sub>2</sub>-H Bond Angle || 119.6735<sup>o</sup> || 118.981<sup>o</sup> || 118.4<sup>o</sup>
|-
| C2-C3-C4-C5 Dihedral Angle || -179.9889<sup>o</sup> || -180.0000<sup>o</sup> || -178.3<sup>o</sup>
|}

It could be seen that B3LYP/6-31G* method was much more accurate than the HF/3-21G method because the bond length and bond angles were more close to the literature value, and also the dihedral angles of C2, C3, C4 and C5 was exactly 180<sup>o</sup>.

===Optimization of an Allyl Fragment===

===Optimization of the 'chair' Transition State===
====First Approach: Optimization to a TS (Berny)====

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

File:1.5 HEXADIENE.PNG

2013-12-06T10:37:29Z

Dd611:

Rep:Mod:yixingphysical

2013-12-06T03:02:34Z

Dd611: /* Results and Discussion */

Rep:Mod:yixingphysical

2013-12-06T02:47:00Z

Dd611:

Rep:Mod:yixingzzang1007

2013-12-06T02:27:51Z

Dd611:

[[Image:Cope arrrrrangment.PNG]]

Rep:Mod:yixingzzang1007

2013-12-06T02:25:38Z

Dd611: /* Cope Rearrangement */

Rep:Mod:yixingphysical

2013-12-04T21:11:13Z

Dd611: /* Optimization of Exo Product */

==Cope Rearrangement==
===Introduction===

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

'''3.Geometry Comparison'''

===Optimization of an Allyl Fragment===

===Optimization of the 'chair' Transition State===
====First Approach: Optimization to a TS (Berny)====

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Product'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.

[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>

[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====

Rep:Mod:yixingphysical

2013-12-04T21:07:48Z

Dd611: /* Optimization of Exo Product */

==Cope Rearrangement==
===Introduction===

[[Image:Cope arrrrrangment.PNG]]

===Optimizations of Reactants and Products===
====Optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1. Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>1,5-hexadieneeeee.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69253528 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001891
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 32.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.036873D-08
Optimization completed.
-- Stationary point found.
</pre>
To check if the job has been successfully converged, an 'Item' table is shown above. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

'''4.File Link'''

To access the .log file of optimization, click [[Media:222222222.LOG|anti 1,5-hexadiene 3-21G]].

====Re-optimizations of Anti-Peri Planar Conformer of 1,5-hexadiene====
'''1.Optimized Anti Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>631Gd mol.mol</uploadedFileContents>
</jmolApplet></jmol>
'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Anti 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61170280 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001326
|-
| Dipole Moment ||0.0000
|-
| Point Group || Ci
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 9.0 seconds
|}

'''3. Validity of Result'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588856D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.469212
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461856
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000036 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000228 0.001800 YES
RMS Displacement 0.000105 0.001200 YES
Predicted change in Energy=-1.497856D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:631 optimmmm.LOG|here]]; for the .log file of frequency analysis, click [[Media:FINAL FREQ.LOG|here]].

====Optimizations of Gauche (3) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69266122 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000702
|-
| Dipole Moment ||0.3405
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 29.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000934 0.001800 YES
RMS Displacement 0.000298 0.001200 YES
Predicted change in Energy=-8.790932D-09
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH333E1ST HF321G.LOG|here]]

====Re-optimizations of Gauche(3) Conformer of 1,5-hexadiene====

'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE31ST 631.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61132934 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00000382
|-
| Dipole Moment ||0.1383
|-
| Point Group || C1
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 30.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Predicted change in Energy=-1.500532D-09
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000668 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.980461D-09
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.468693
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.461464
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCH3E1ST 631.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE3331ST 631 FREQ.LOG|here]].

====Optimizations of Gauche (4) Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST HF321G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''

{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.69153034 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001325
|-
| Dipole Moment ||0.1280
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 4.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001439 0.001800 YES
RMS Displacement 0.000540 0.001200 YES
Predicted change in Energy=-2.875776D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST HF321G.LOG|here]]

====Re-optimizations of Gauche Conformer of 1,5-hexadiene====
'''1. Optimized Gauche Structure'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>ANNYGAUCHE1ST 6-31G.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Results'''
{| class="wikitable" border="1"
|+
| Molecule || Gauche 1,5-hexadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -231.61048196 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001090
|-
| Dipole Moment ||0.1383
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 47.0 seconds
|}

'''3. Validity of Results'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000457 0.001800 YES
RMS Displacement 0.000144 0.001200 YES
Predicted change in Energy=-1.213327D-08
Optimization completed.
-- Stationary point found.
</pre>
'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000450 0.001800 YES
RMS Displacement 0.000180 0.001200 YES
Predicted change in Energy=-1.181951D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees) = -234.467784
Sum of electronic and thermal Energies at 298.15 K (Hartrees) = -234.460521
</pre>

'''5.File Link'''

To access the .log file of optimization, click [[Media:ANNYGAUCHE1ST 6-31G.LOG|here]]; for the .log file of frequency analysis, click [[Media:ANNYGAUCHE1ST 6-31G FREQUENCY.LOG|here]].

====Results and Discussion====
'''1.Symmetry Comparison'''

{| class="wikitable"
|-
| Conformer || Point Group || Literature Point Group
|-
| Anti 2 || Ci || Ci
|-
| Gauche 3 || C1 || C1
|-
| Gauche 4 || C2 || C2
|}

According to the table above, all optimization jobs have been successfully finished because they all generated the correct symmetry point groups. It should be noticed that all point groups were C1 if the log file was opened; this was due to the feature of the program which altered the symmetry in order to have the minimum energy.

'''2.Thermochemistry Comparison'''

'''3.Geometry Comparison'''

===Optimization of an Allyl Fragment===

===Optimization of the 'chair' Transition State===
====First Approach: Optimization to a TS (Berny)====

'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair opt+freq 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -231.61932247 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.93 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:818 frequency movie.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:CHAIR OPT+FREQ 1ST TRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

'''6. IRC Calculation'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932247 a.u.
|-
| Gradient || 0.00000569 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:C111111apture.PNG|700px]]

According to the graphs above, RMS gradient only had a trend of converging to zero, but not actually reach zero. Therefore, further analysis had to be done in order to give a more accurate result.

There are three approaches which have been done to get reliable results:

Method 1: run an optimization calculation of the last point on the IRC. This approach is the fastest but it is not accurate enough to reach a minimum energy and may also locate a wrong result due to the uncertainty of the endpoint.

Method 2: redo the IRC calculation with a larger number of points (in this case, 150). This approach is more reliable than method 1 but also has risk of resulting in the wrong structure due to too many points involved.

Method 3: redo IRC calculation with computing the force constants at every steps. This approach is the most reliable but is not always working for the large systems.

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.69166702 a.u.
|-
| Gradient || 0.00000475 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:1ST METHOD.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.61932200 a.u.
|-
| Gradient || 0.00000581 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Method 2 capture.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:2ND METHOD.LOG|here]].

====Re-optimization to a TS (Berny) using B3LYP/6-31G* Level of Theory====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)+ Frequency Analysis
|-
| Basis Set || B3LYP/6-31G(d)
|-
| Total Energy || -234.55698303 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.54 cm<sup>-1</sup>
|}

'''2. Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-3.752833D-09
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -234.414929
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -234.409009
</pre>

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Reopt 1st approach movie.gif]]

'''4.File Link'''

To access to the .log file of optimization, click [[Media:ReoptCHAIR OPT+FREQ 1ST TRY.LOG|here]].

====Second Approach: Optimization to a TS(Berny) with Frozen Coordinates====
'''1. Optimized Chair Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>3RDPPROACHSTTRY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS (Berny)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Keyword || Opt=NoEigen
|-
| Total Energy || -234.55698246 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -565.63 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Moivvvvveee.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:3RDAPPROACH1STTRY.LOG|here]]

'''5. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000122 0.001200 YES
Predicted change in Energy=-8.556510D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)= -231.466700
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.461340
</pre>

====Third Approach: Optimization to a TS (Berny)with Derivative====

'''1.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Chair
|-
| Method || Optimization to a TS with Derivative
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Total Energy || -231.61932238 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -817.90 cm<sup>-1</sup>
|-
| Point Group || C<sub>2h</sub>
|}

'''2.Vibration Mode of Imaginary Frequency'''

[[Image:818 vibration 3rd try.gif]]

'''3.File Link'''

To access to the .log file of optimization, click [[Media:3RDPPROACH1STTRY.LOG|here]].

'''4. Frequency Analysis'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001483 0.001800 YES
RMS Displacement 0.000503 0.001200 YES
Predicted change in Energy=-1.010179D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energiesat 0 K (Hartrees)=-231.466696
Sum of electronic and thermal Energies298.15 K (Hartrees)=-231.461337
</pre>

===Optimization of the 'boat' Transition State===
====First Approach: Optimization from Anti 2 Conformer====

First of all, optimization to TS(QTS2) was done by using the anti-conformer which had Ci symmetry as both reactant and product.
As the numbering of carbon atoms would change during the reaction, the number of atoms were changed manually as shown in the following figure.

[[Image:Two failed numbering.PNG|400px]]

However, the optimization job failed according to the chk file, because the transition state looked like the chair transition structure. This was due to the ignorance of the possibility of central bond rotation. The calculation simply translated the top allyl fragment; therefore, the QST2 method would not be able to locate the transition state of boat structure successfully without modification of the structures of reactants and products.

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Boat QST2 1st try.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Two failed numbering 2.PNG|300px]]

====Second Approach: Optimization with Modified Reactant and Product====
In order to locate the 'boat' transition state, structures of both reactants and products have been modified as shown below. The central C2-C3-C4-C5 dihedral angle was changed to be 0<sup>o</sup> and the bond angle of C2-C3-C4 as well as C3-C4-C5 were changed to be 100<sup>o</sup>.

[[Image:11111111111Capture.PNG]]

[[Image:2nd try qts2.PNG]]

'''1. Optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;measure 3 4</script>
<uploadedFileContents>Boat ts qst2 2nd try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS(QTS2)
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.60280200 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -839.94 cm<sup>-1</sup>
|-
| Point Group || C<sub>2v</sub>
|}

'''3. Vibration Mode of Imaginary Frequency'''

[[Image:Boat qst2 2nd try gif vibration.gif]]

'''4.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001453 0.001800 YES
RMS Displacement 0.000438 0.001200 YES
Predicted change in Energy=-4.886062D-07
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies at 0 K (Hartrees)=-231.450928
Sum of electronic and thermal Energies at 298.15 K (Hartrees)= -231.445299
</pre>
'''5.File Link'''

To access to the .log file of optimization, click [[Media:BOAT TS QST2 2ND TRY.LOG|here]].

'''6. IRC Calculation'''

[[Image:IRC movie boat.gif]]

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 50
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.60280200 a.u.
|-
| Gradient || 0.00007077 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:11111111Capture.PNG||700px]]

To access to the .log file of IRC calculation, click [[Media:IRCBOAT TS QST2 2ND TRY.LOG|here]].

'''Method 1. Optimization of the IRC Endpoint'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to minimum (RHF)
|-
| Basis Set || HF/3-21G
|-
| Total Energy || -231.68302550 a.u.
|-
| Gradient || 0.00000769 a.u.
|}
To access to the .log file of optimization calculation of endpoint,click [[Media:METHOD 1.LOG|here]].

'''Method 2. IRC Calculation with Larger Number of Points'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.68393048 a.u.
|-
| Gradient || 0.00042262 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 2.PNG|700px]]

To access to the .log file of IRC calculation,click [[Media:Boat2ND METHOD.LOG|here]].

'''Method 3. Calculating Force Constant at Each Step'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || IRC
|-
| Basis Set || HF/3-21G
|-
| Number of Points || 150
|-
| Direction || Forward Only
|-
| Energy of Last Point || -231.67591436 a.u.
|-
| Gradient || 0.00114584 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Capture method 3.PNG|700px]]

====Re-optimization to boat TS using B3LYP/6-31G* Level of Theory====

'''1. Re-optimized Boat Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Reopt qts2 boat.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Type of Transition State || Boat
|-
| Method || Optimization to a TS (QTS2)
|-
| Basis Set || B3LYP/6-31G*
|-
| Total Energy || -234.54309304 a.u.
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -530.57 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
Predicted change in Energy=-3.598582D-08
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396005
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

[[Image:BOAT REOPT MOVIE.gif]]

====Results and Discussion====

'''1.Geometry Comparison'''

'''2. Thermochemistry Comparison'''

===Discussion===
==Diels Alder Cycloaddition==
===Introduction===
===Reaction Between Ethylene and Cis-Butadiene===
====Optimization of Reactants====
'''1. Optimization of Cis-butadiene'''

'''1.1 Optimized Cis-butadiene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Optimization of butadiene anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cis-butadiene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.04879719 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 21.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000408 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691119D-09
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF BUTADIENE ANNY.LOG|here]].

'''1.5 HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:AnnyButadiene lumo.PNG|300px]]|| [[File:AnnyButadiene homo.PNG|300px]]
|-
|LUMO||HOMO
|}

'''2. Optimization of Ethylene'''

'''1.1 Optimized Ethylene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>OPTIMIZATION OF ETHYLENE ANNY.mol</uploadedFileContents>
</jmolApplet></jmol>

'''1.2 Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Ethylene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.02619028 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00003647
|-
| Dipole Moment ||0.0000
|-
| Point Group || D<sub>2h</sub>
|-
| Jop cpu Time ||0 days 0 hours 0 minutes 3.0 seconds
|}

'''1.3 Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000178 0.000450 YES
RMS Force 0.000053 0.000300 YES
Maximum Displacement 0.000441 0.001800 YES
RMS Displacement 0.000236 0.001200 YES
Predicted change in Energy=-5.173658D-08
Optimization completed.
-- Stationary point found.
</pre>

'''1.4 File Link'''

To access the .log file of optimization, click [[Media:OPTIMIZATION OF ETHYLENE ANNY.LOG|here]].

====Analysis of Transition States====
'''Optimization of Transition State using AM1 Semi-Empirical'''

'''1.Optimized Transition State'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts 2try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2.Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || TS
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO (AM1 semi-empirical)
|-
| Total Energy || 0.11165470 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00004118
|-
| Dipole Moment ||0.5610
|-
| Point Group || C<sub>s</sub>
|-
| Number of Imaginary Frequency || 1
|-
| Wavenumber of Imaginary Frequency || -957.06 cm<sup>-1</sup>
|}

'''3.Vibration Mode of Imaginary Frequency'''

[[Image:Ts 95706.gif]]

'''4. File Link'''

To access to the .log file of optimization, click [[Media:TS 2TRY.LOG|here]]

'''5. HOMO LUMO Molecular Orbitals'''

{| class="wikitable" border="1"
|+
| [[File:TS LUMO.PNG|300px]]|| [[File:TS HOMO.PNG|300px]]
|-
|LUMO(Symmetric)||HOMO(Antisymmetric)
|}
'''IRC Calculation of Transition State using AM1 Semi-Empirical'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Ts IRC 1ST RESULT.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || AM1 semi-empirical
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || 0.07462805 a.u.
|-
| Gradient || 0.00004570 a.u.
|}

Total Energy and RMS gradient graph:

[[Image:Captureeeeeeee.PNG|700px]]

[[Image:Irc_movvviieeeee.gif]]

To access to the .log file of IRC calculation,click [[Media:TS_IRC_1ST.LOG|here]].

'''Optimization of Transition State using 6-31G(d) Basis Set'''

'''IRC Calculation of Transition State using 6-31G(d) Basis Set'''

{| class="wikitable" border="1"
|+
| Method || IRC
|-
| Basis Set || 6-31G(d)
|-
| Number of Points || 100
|-
| Direction || Both directions
|-
| Energy of Last Point || -234.57525785 a.u.
|-
| Gradient || 0.00007561 a.u.
|}

====Results and Discussion====

===Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride===
[[Image:Endo exo mechanismm.PNG]]
====Optimization of Reactants====
=====Optimization of Maleic Anhydride=====
'''1. Optimized Maleic Anhydride Molecule'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>MA opt631 anny.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Maleic Anhydride
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -379.28954412 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001745
|-
| Dipole Moment ||0.0414
|-
| Point Group || C<sub>2v</sub>
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000292 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000551 0.001200 YES
Predicted change in Energy=-4.590331D-07
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:MA_OPT631_ANNY.LOG|here]].

=====Optimization of Cyclohexa-1,3-diene=====
'''1. Optimized Cyclohexa-1,3-diene'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYC13_631GOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable" border="1"
|+
| Molecule || Cyclohexa-1,3-diene
|-
| Method || Optimization to a minimum
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Total Energy || -233.41893629 a.u.
|-
| Charge || 0
|-
| Gradient || 0.00001902
|-
| Dipole Moment ||0.3780
|-
| Point Group || C2
|-
| Jop cpu Time ||0 days 0 hours 1 minutes 18.0 seconds
|}

'''3. Validity of Result'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000547 0.001800 YES
RMS Displacement 0.000155 0.001200 YES
Predicted change in Energy=-3.186501D-08
Optimization completed.
-- Stationary point found.
</pre>

'''4.File Link'''

To access the .log file of optimization, click [[Media:CYC13_631GOPT.LOG|here]].

====Optimization of Exo Product====

'''1. Optimized Exo Adduct'''

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXOTS_1st_try.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. Key Information of Result'''

{| class="wikitable"
|-
| Method || Optimization to TS(Berny) + Frequency
|-
| Basis Set || ZDO(AM1 semi-empirical)
|-
| Key Word || opt=noeigen
|-
| Total Energy || -0.05041985 a.u.
|-
| Number of Imaginary Frequencies || 1
|-
| Wavenumber of imaginary Frequency || -812.21 cm<sup>-1</sup>
|}

'''3.Frequency Analysis'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-1.390869D-11
Optimization completed.
-- Stationary point found.
</pre>
<pre>
Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
</pre>

'''4.Vibration Mode of Imaginary Frequency'''

Imaginary frequency was at -812.21 cm<sup>-1</sup>.
[[File:821imaginary freq move.gif]]

'''5 Vibration Mode of First Positive Frequency'''

First real frequency was at 60.85 cm<sup>-1</sup>
[[File:6085 first vibra movie.gif]]

'''6. File Link'''

To access the file link to .log file of optimization, click [[Media:EXOTS 1ST TRY.LOG|here]]

====Optimization of Endo Product====
====Result and Discussion====