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Rep:Mod:mh2710tata2

2014-03-20T11:51:35Z

Mh2710: Blanked the page

Rep:Mod:qwt11

2014-01-30T23:14:51Z

Mh2710: /* Analysis of the properties of the synthesised alkene epoxides */

Rep:Mod:qwt11

2014-01-30T23:10:57Z

Mh2710: /* Spectroscopic Simulation using Quantum Mechanics */

Experiment 1C: Organic Computational Lab

'''
== The Hydrogenation of Cyclopentadiene Dimer ==

'''Kinetic control VS Thermodynamic control'''

<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>1 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 1<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>2 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 2
<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>3 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 3
<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>4 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 4

Cyclopentadiene dimerises to an endo dimer and an exo dimer, 1&2. Hydrogenation of these two dimers proceeds to give two relative derivatives 3&4. The aim is to distinguish which product undergoes a thermodynamic or a kinetic reaction. A series of chemical related tools are used. “Chembio3D” shows both planar and stereo versions of molecules. "Gaussview" uses to display predicted NMR spectra. Under the help of “Avogadro”, a few types of crucial energy obtain, such as total bond stretching energy, total angle bending energy, total stretch bending energy, total torsional energy, total out-of-plane bending energy, total Van der Waals energy, total electrostatic energy and total energy (sum) of a particular. These information are allocated and the table below lists them out.

{| class="wikitable" border="1"
|+ Comparison of the results
! Property !! Dimer 1 (kcal/mol)!! Dimer 2 (kcal/mol) !! Dimer 3 (kcal/mol) !! Dimer 4 (kcal/mol)
|-
| Total bond stretching energy || 3.54360 || 3.46789 || 3.31086 || 2.93009
|-
| Total angle bending energy || 30.77335 ||33.18937 || 31.92713 || 21.09197
|-
| Total stretch bending energy || -2.04136 || -2.08218 || -2.10106 || -1.70918
|-
| Total torsional energy || -2.73744 || -2.94947 || -1.46254 || 0.17128
|-
| Total out-of-plane bending energy || 0.01469 || 0.02183 || 0.01315 || 0.00051
|-
| Total Van der Waals energy || 12.80707 || 12.35873 || 13.63924 || 10.68113
|-

| Total electrostatic energy || 13.01379 || 14.18450 || 5.11948 || 5.14891
|-
| Total energy || 55.37368 || 58.19067 || 50.44627 || 38.31470
|}

[[image:1234hydrogenation.png|thumb|left|470x470px|Hydrogenation of Cyclopentadiene]]

According to the table above, we clearly see that total energy (55.37368kcal/mol) of dimer 2 (55.37368kcal/mol) stays below while compare with dimer 1, which means dimer 1 is thermodynamic stable (ie: product stability) and dimer 2 is kinetic stable (ie: transition state stability). Likewise hydrogenated compound 3 gains more stability when it acts as a transition state and compound 4 prefers to act as a product. On the other hand, two indicated hydrogens senses more steric effect by the double bond in molecule 3, hence the higher total energy and less stable.

== '''Atropisomerism in an Intermediate related to the Synthesis of Taxol.''' ==
[[image:9 10.png|thumb|right|470x470px|Atropisomerism of Intermediate of Taxol]]
<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>9 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Intermediate9<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>10 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Intermediate10
{| class="wikitable" border="1"
|+ Comparison of the results
! Property !! Intermediate 9 (kcal/mol)!! Intermediate 10 (kcal/mol)
|-
| Total bond stretching energy || 7.70017 || 7.91408
|-
| Total angle bending energy || 28.29773 || 20.97586
|-
| Total stretch bending energy || -0.06950 || -0.06081
|-
| Total torsional energy || 0.10769 || 4.45974
|-
| Total out-of-plane bending energy || 0.98074 || 0.95594
|-
| Total Van der Waals energy || 33.24245 || 34.75428
|-
| Total electrostatic energy || 0.29497 || -0.04407
|-
| Total energy || 70.55425 || 68.95502
|}

Due to total energy shown on this table, we easily determine molecule 10 is more stable since it owns relatively lower total energy. On the other hand, we find that all the energy between two intermediates are virtually the same expect for the total angle bending energy. By using “Avogadro”, we prove that the angle between C-O-C(carbon on six-membered ring) for compound 10 is 108.5。 which exactly matches the angle of sp3 hybridization, however, the angle distorts to 117.5。 for compound 9 while a large gap indicates. Therefore, the final total energy of molecule 9 remains at a relatively high level.
Here is the proof:
[[image:9 angle.png|thumb|left|470x470px|Intermediate 9]]
[[image:10 angle.png|thumb|right|540x600px|Intermediate 10]]

Futhermore, for the reason that why alkenes particular for 9 and 10 react slowly. A new class of “hyperstable” olefins can now be defined, olefins which contain less strain than that of the parent hydrocarbon and have negative OS values. Such olefins should be very unreactive-not due to steric hindrance3’ or to enhanced a-bond strength but due to special stability afforded by the cage structure of the olefin and to the greater strain of the parent polycycloalkane.[1]

== '''Analysis of the properties of the synthesised alkene epoxides''' ==

(I) Catalyst Structures 
The stable precursor (21) of the Shi catalyst shown below was synthesised for the epoxidation of styrene and trans-B-methyltyrene.

<center>[[File:Molecule_21_sticks.png|350px|]] 
'''Figure 3.1''': Molecule 21 with labelled bond lengths and angles</center> 

<center>[[File:Molecule_21.png|400px|]] 
'''Figure 3.2''': Stick diagram of molecule 21 with the C-O bond lengths</center> 

Close examination of the C-O bond lengths in the anomeric centres with O-C-O substructures found that one C-O bond is significantly longer than the other. This is presented in Figure 3.2, where the bottom anomeric centre shows C-O bond lengths of 1.428Å and 1.456Å, when the expected bond length is 1.43Å. This is similarly found in the top anomeric structure. In addition, the terminal methyl groups are found to have shorter than normal C-C bonds (1.54Å) with values ranging from 1.500Å - 1.511Å. This observation is likely due to overlap of the p* orbitals in O atoms that have weak C-O bonds and the sp3 orbitals in C atoms. As a result the bonding orbitals of the C atoms are stabilised, resulting in stronger C-C bonds while the donation of some electron density to the p* orbital due to the overlap decreases the bond order and weakens the C-O bond. The O-C-O angles are also observed to be smaller than the expected value of 109.5o. The anomeric centre that is contained in both the 5-membered ring and 6-membered ring has shorter than normal C-O bonds with values of 1.415Å and 1.423Å. The short C-O bond can be explained by the resonance effect to the nearby C=O group. 

For the Jacobsen asymmetric catalyst, the stable pre-catalyst (23) formed in the reaction is shown below. 

<center>[[File:Molecule2301.png|250px|]] 
'''Figure 3.3''': Molecule 23</center> 

<center>[[File:Molecule_23_stick_and_ball.png|350px|]] 
'''Figure 3.4''': Sticks and ball diagram of molecule 23</center> 

Referring to Figure 3.4, a close approach of the 2 adjacent t-butyl groups on the rings is observed. When the shortest distance between the protons were measured, it was found to be 2.421Å, which corresponds to the Van Der Waals radii for the maximum attractive interaction<ref name="conformationalanalysis">H. S. Rzepa, 2010.</ref>. This helps to stabilise the molecule strongly. The dominance of the strong H...H Van Der Waals interactions is further supported by the fact that it is present despite the close proximity that results in repulsive O..H Van der Waals interactions (2.335Å and 2.193Å) being observed too. 

The rest of the report will be based on the (R) and (S) styrene oxides and the (R)(R), (S)(S), (R)(S), (S)(R) trans-ß-Methylstyrene oxides.

(II) NMR of selected epoxides 
The NMR spectra of the selected epoxides were computed and the calculated chemical shifts were compared with those found in literature as no NMR spectra of the epoxides were produced in the actual synthesis. 
 
(R)-Styrene oxide 
The (S)-Styrene oxide produces the same NMR data as the (R)-Styrene oxide and will not be shown below. 
<center>[[File:R_Styrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.1''': Labelled atoms of (R)-Styrene oxide 

[[File:R_Styrene_oxide_NMR_1H.svg|800px|]] 
'''Figure 4.2''': 1H NMR spectrum of (R)-Styrene oxide 

[[File:R_Styrene_oxide_1H_NMR_table.png|500px|]]
Table 3.1: Table illustrating the calculated shifts for 1H NMR of (R)-Styrene oxide<ref name="j.tetasy.2009.005.001">K. Sarma, A. Goswamia, and B. C. Goswamib, Tetrahedron, 2009, 20, 1295–1300.{{DOI|10.1016/j.tetasy.2009.005.001}}</ref> </center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="j.tetasy.2009.005.001" /> with insignificant derivations of <0.20ppm. Precision is seen in the calculated values which indicate that proton #13 has a different chemical shift than the rest of the protons. This is likely due to the close proximity of proton #13 with the O atom. However, protons #11 and #14 should not have the same chemical shift as protons #10 and #12 as they are not chemically equivalent. 

<center>[[File:R_Styrene_oxide_NMR_13C.svg|800px|]] 
'''Figure 4.3''': 13C NMR spectrum of (R)-Styrene oxide 

[[File:R_Styrene_oxide_13C_NMR_table.png|500px|]]
Table 3.2: Table illustrating the calculated shifts for 13C NMR of (R)-Styrene oxide<ref name="j.tetasy.2009.005.001" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="j.tetasy.2009.005.001" /> with insignificant derivations of <5.00ppm. The literature failed to report 2 of the chemical shifts for the protons, likely due to its close proximity on the spectra that results in overlaps. 

(R),(R)-trans-ß-Methylstyrene oxide 
The (S),(S)-trans-ß-Methylstyrene oxide produces the same NMR data as the (R),(R)-trans-ß-Methylstyrene oxide and will not be shown below. 
<center>[[File:2R,3R-trans-ß-Methylstyrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.4''': Labelled atoms of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_1H_NMR.svg|800px|]] 
'''Figure 4.5''': 1H NMR spectrum of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_1H_NMR_table.png|500px|]]
Table 3.3: Table illustrating the calculated shifts for 1H NMR of (R),(R)-trans-ß-Methylstyrene oxide<ref name="jo900739q">O. Andrea Wong, B. Wang, M.-X. Zhao, and Y. Shi, Journal of Organic Chemistry , 2009, 74, 6335–6338.{{DOI|10.1021/jo900739q}}</ref></center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="jo900739q" />. Protons #18-20 were reported to have 3 different chemical shifts despite belonging to a -CH3 group. This indicates that the computed results took into account that presence of slow rotation about the C atom due to the hindrance of the O atom which results in the 3 protons being seen as having different environments. Additionally, the aromatic proton #15 does not have the same chemical shift as proton #14 despite being in the same chemical environment. This implies that they are magnetically inequivalent. This is possible if there's slow rotation about the C(Ph)-C(OC) bond. 

<center>[[File:2R,3R-trans-ß-Methylstyrene_oxide_13C_NMR.svg|800px|]] 
'''Figure 4.6''': 13C NMR spectrum of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_13C_NMR_table.png|500px|]]
Table 3.4: Table illustrating the calculated shifts for 13C NMR of (R),(R)-trans-ß-Methylstyrene oxide<ref name="jo900739q" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="jo900739q" />. As seen previously, the computed results show individual chemical shifts for the aromatic carbons which is not seen in the literature. 

(R),(S)-trans-ß-Methylstyrene oxide 
The (S),(R)-trans-ß-Methylstyrene oxide produces the same NMR data as the (R),(S)-trans-ß-Methylstyrene oxide and will not be shown below. 
<center>[[File:2S,_3R-trans-ß-Methylstyrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.7''': Labelled atoms of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_1H_NMR.svg|800px|]] 
'''Figure 4.8''': 1H NMR spectrum of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_1H_NMR_table.png|500px|]]
Table 3.5: Table illustrating the calculated shifts for 1H NMR of (R),(S)-trans-ß-Methylstyrene oxide<ref name="anie.201201848">S. Koya, Y. Nishioka, H. Mizoguchi, T. Uchida, and T. Katsuki, Angewandte Chemie International Edition, 2012, 51, 8243–8246.{{DOI|10.1002/anie.201201848}}</ref></center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="anie.201201848" />. The observation for (R),(R)-trans-ß-Methylstyrene oxide is also seen here; protons #11, 12 and 20 are found to be of different chemical shifts despite belonging to the same -CH3 group. Similarly, protons #15 and 19 are calculated to have different chemical shifts despite being chemically equivalent, implying that they are magnetically inequivalent. 

<center>[[File:2S,3R-trans-ß-Methylstyrene_oxide_13C_NMR.svg|800px|]] 
'''Figure 4.9''': 13C NMR spectrum of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_13C_NMR_table.png|500px|]]
Table 3.6: Table illustrating the calculated shifts for 13C NMR of (R),(S)-trans-ß-Methylstyrene oxide<ref name="anie.201201848" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="anie.201201848" />. As seen previously, the computed results show individual chemical shifts for the aromatic carbons which is not seen in the literature. 

(III) Calculated chiroptical properties of selected epoxides 
The optical rotation values were calculated for 3 different epoxides; their respective enantiomers were assumed to have the same values but of different signs. No comparison is made with experimental results as none were produced due to the lack of time, hence comparison is made with litera 

<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Epoxides
! style="background: #fdb813; color: black;" |Calculated values of [α]D (o)
! style="background: #fdb813; color: black;" |Reported values of [α]D (o)
|-
| (R)-Styrene Oxide
| style="text-align: center;" |-179.79
| style="text-align: center;" |-23.7<ref name="j.tetasy.2003.09.024">D. E. White and E. N. Jacobsen, Tetrahedron, 2003, 14, 3633–3638.{{DOI|10.1016/j.tetasy.2003.09.024}}</ref>
|-
| (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |+131.77
| style="text-align: center;" |+44.3<ref name="jo900739q" />
|-
| (S),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |+33.99
| style="text-align: center;" |+38.6<ref name="anie.201201848" />
|}
</center>
<center>Table 4.1: Table showing the epoxides and their calculated optical rotations</center> 
The calculated values of [α]D (o) all show the same sign as the ones reported. However, the computed value for (R)-Styrene oxide largely deviates from the literature value, with a difference of 157o. Similarly, the computed value for (R),(R)-trans-ß-Methylstyrene oxide also deviates from the literature by 87o. Only the computed value for (S),(R)-trans-ß-Methylstyrene oxide is close to the value reported. Since the specific optical rotation already takes into account the path length and the concentration of the molecules, the large deviation is likely due to the difference in conformations between the ones used for calculations and the ones done in experiment. This is because the computed values differ for different conformers of the same compound. At the same time, it is also possible that the deviation is due to presence of impurities during measurement in the experiment. This is because the epoxides are produced in a racemic mixture and separation is required before measuring the optical rotation. Hence it is difficult to evaluate the accuracy of the computed results and the literature results as different literature reports produce different values too. One way of improving the computed results will be to repeatedly produce optimised molecules for computation. 

 
(IV) Using the properties of transition state for the reaction 
Shi catalyst transition states 
Trans-ß-Methylstyrene oxide and styrene oxide were chosen for this segment. 

Out of the 8 transition states provided for the (R),(R)-trans-ß-Methylstyrene oxide and the (S),(S)-trans-ß-Methylstyrene oxide, the ones with the lowest energies, i.e. largest magnitude since G<0, were chosen for further calculations. This is because the lowest energies transition states are the most stable and will most likely occur to give the epoxides. The values obtained from the .log files were also converted from Hartree/particle to Joules/mol.

<center>
{| class="wikitable"
| G of (R),(R)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-1343.032443
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-1343.024742
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-3.5261343E+09
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-3.5261341E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.02E+04
|-
| K ([(R),(R) enatiomer]/[(S),(S) enantiomer])
| style="text-align: center;" |3485.09
|-
| Ratio of (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |0.9997
|-
| Ratio of (S),(S)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |2.869E-04
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.9
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |96-98<ref name="Shi01">Z.-X. Wang, L. Shu, M. Frohn, Y. Tu, and Y. Shi, Organic Syntheses, 2003, 80, 9.</ref>
|}
</center>
<center>Table 5.1: Table showing calculations for the transition states for the epoxidation of trans-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.02E+04 Joules/mol, implying that (R),(R)-trans-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (R),(R)-trans-ß-Methylstyrene oxide over (S),(S)-trans-ß-Methylstyrene oxide is denoted as K and given to be 3485.09. Since the ratio of both concentrations add up to 1, the predicted enantiomer excess is calculated to be 99.9% with the (R),(R)-trans-ß-Methylstyrene oxide being the dominating enantiomer. This is in line with the reported value of 96-98% by Shi<ref name="Shi01" /> 

<center>
{| class="wikitable"
| G of (R)-styrene oxide (Hartree/Particle)
| style="text-align: center;" |-1303.738044
|-
| G of (S)-styrene oxide (Hartree/Particle)
| style="text-align: center;" |-1303.738503
|-
| G of (R)-styrene oxide (Joules/mol)
| style="text-align: center;" |-3.422967E+09
|-
| G of (S)-styrene oxide (Joules/mol)
| style="text-align: center;" |-3.422968E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |1.21E+04
|-
| K ([(R) enantiomer]/[(S) enatiomer])
| style="text-align: center;" |0.615
|-
| Ratio of (R)-styrene oxide
| style="text-align: center;" |0.619
|-
| Ratio of (S)-styrene oxide
| style="text-align: center;" |0.381
|-
| Enantiomeric excess (%)
| style="text-align: center;" |23.8
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |24.3<ref name="Shi02">Z.-X. Wang, Y. Tu, M. Frohn, J.-R. Zhang, and Y. Shi, Journal of the American Chemistry Society, 1997, 119, 11224–11235.{{DOI|10.1021/ja972272g}}</ref>
|}
</center>
<center>Table 5.2: Table showing calculations for the transition states for the epoxidation of styrene </center> 
The difference in free energies (∆G) is calculated to be 1.21E+04 Joules/mol, implying that (S)-styrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (R)-styrene oxide over (S)-styrene oxide is denoted as K and given to be 0.615. The predicted enantiomer excess is calculated to be 23.8% with the (R)-styrene oxide being the dominating enantiomer. This is also in line with the reported value of 24.3% by Shi<ref name="Shi02" />. 

Jacobsen catalyst transition states 
<center>
{| class="wikitable"
| G of (S),(R)-cis-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.259559
|-
| G of (R),(S)-cis-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.25106
|-
| G of (S),(R)-cis-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88275E+09
|-
| G of (R),(S)-cis-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88273E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.23E+04
|-
| K ([(S),(R)enantiomer]/[(R),(S) enantiomer])
| style="text-align: center;" |8114.63
|-
| Ratio of (S),(R)-cis-ß-Methylstyrene oxide
| style="text-align: center;" |1.23E-04
|-
| Ratio of (R),(S)-cis-ß-Methylstyrene oxide
| style="text-align: center;" |0.9999
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.9%
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |92<ref name="ja00018a068">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. , Ecker, and L. Deng, Journal of the American Chemistry Society, 1991, 113, 7063–7064.{{DOI|10.1021/ja00018a068}}</ref>
|}
</center>
<center>Table 5.3: Table showing calculations for the transition states for the epoxidation of cis-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.23E+04 Joules/mol, implying that (S),(R)-cis-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (S),(R)-cis-ß-Methylstyrene oxide over (R),(S)-cis-ß-Methylstyrene oxide is denoted as K and given to be 8114.63. The predicted enantiomer excess is calculated to be 99.9% with the (R),(S)-cis-ß-Methylstyrene oxide being the dominating enantiomer. This is slightly higher than the experimental results by Jacobsen<ref name="ja00018a068" /> but it still ties in with the observation that the (R),(S)-cis-ß-Methylstyrene oxide is preferentially formed. 

<center>
{| class="wikitable"
| G of (S),(S)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.262481
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.254344
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88276E+09
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88274E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.14E+04
|-
| K ([(S),(S)enantiomer]/[(R),(R) enantiomer])
| style="text-align: center;" |5530.45
|-
| Ratio of (S),(S)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |0.9998
|-
| Ratio of (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |1.81E-04
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.96
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |92<ref name="ol0069406">A. M. Daly, M. F. Renehan, and D. G. Gilheany, Organic Letters, 2001, 3, 663–666.{{DOI|10.1021/ol0069406}}</ref>
|}
</center>
<center>Table 5.4: Table showing calculations for the transition states for the epoxidation of trans-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.14E+04 Joules/mol, implying that S),(S)-trans-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of S),(S)-trans-ß-Methylstyrene oxide over (R),(R)-trans-ß-Methylstyrene oxide is denoted as K and given to be 5530.45. The predicted enantiomer excess is calculated to be 99.96% with the (S),(S)-trans-ß-Methylstyrene oxide being the dominating enantiomer. This is slightly higher than the literature value of 92% but the preference for the formation of (S),(S)-trans-ß-Methylstyrene oxide is supported. 

(V) Investigating the non-covalent interactions in the active-site of the reaction transition state 
 The (R),(R)-trans-ß-Methylstyrene oxide transition state using the Shi catalyst is chosen for this analysis. 

<center>[[File:RRNCIfile.png|500px|]] 
'''Figure 5.1''': NCI analysis of the transition state using Shi catalyst to form (R),(R)-trans-ß-Methylstyrene oxide </center>
 
It can be observed that active site in the Shi catalyst is positioned at one of the dioixirane O atoms. Observation of blue and green electron density near the active site indicates very attractive interaction between the catalyst and the alkene at this position. Specifically, the 5-membered ring on the Shi catalyst shows strong interaction with the protons on the methyl group and the phenyl ring which are positioned closely to the alkene functional group such that they enclose it. In addition, the dioxirane O atom that is not involved in the epoxidation shows hydrogen bond like interaction with a proton on the protruding methyl group at the other end. Intramolecular hydrogen bonding interaction is also observed in the Shi catalyst between the proton on the methyl group and ether O in the 6-membered ring. These attractive interactions help to stabilise the overall system and are a result of an endo-type interaction between the dioxirane O atom and the alkene functional group where the latter is positioned directly above the former. As a result, the epoxidation of the trans-ß-Methylstyrene is a syn addition to the alkene double bond. This explains the formation of the (R),(R)-trans-ß-Methylstyrene oxide enantiomer from this transition state.
 
(VI) Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state 
The electronic topology of the transition state for the formation of (R),(R)-trans-ß-Methylstyrene oxide using Shi catalyst is shown below.
 
<center>[[File:(RR)QTAIM.png|500px|]] 

'''Figure 6.1''': Electronic topology of the transition state using Shi catalyst to form (R),(R)-trans-ß-Methylstyrene oxide </center> 
Atoms that are involved in weak non-covalent bond critical point(BCP) are annotated in Figure 6.1. On close inspection, it is observed that there is an absence of a bond (i.e. BCP not seen) between the dioxirane O atoms in the Shi catalyst. With the lack of a covalent bond, the O atom that is not involved in the epoxidation is stabilised by hydrogen bonding with a proton on the methyl group as it has the most suitable distance for attractive interaction. On the other hand, the O atom involved in epoxidation is stabilised by weak non-covalent interactions with the C atom on the alkene C=C that is less hindered. This illustrates the means of epoxidation. In additional, the overall structure is stablised by favourable weak interactions such as hydrogen bonding between the O atom in the 5-membered ring with suitable H atoms and H...H Van Der Waals interactions.
 

(VII) Suggesting new candidates for investigations 
One alkene that can be epoxidised to give an epoxide with [α]D=835.9o<ref name="jo01045a016">W. Reusch and C. K. Johnson, Journal of Organic Chemistry, 1963, 28, 2557–2560.{{DOI|10.1021/jo01045a016}}</ref> is (+)-pulegone shown below: 
<center>[[File:D-pulegone.png|350px|]] 
'''Figure 7.1''': Epoxidation of (+)-pulegone </center> 
This will give cis R-(+)-pulegone oxide. 

Conclusion 
In conclusion, the use of computational methods has allowed an expansion on the experiment performed for the epoxidation of selected alkenes using Shi catalyst and Jacobsen catalyst. It has proven useful in conformational analysis of specific compounds to explain unexpected observations seen in experiments. Similarly, it also allows the computation of NMR spectra of various optimised molecules which can then be compared with the ones produced in literature. More importantly, it helps to calculate free energies which is use to identify the stability of the molecules. Optical rotation of chiral epoxides were also computed but more can be expanded in this area to ensure its accuracy. Computational methods also allow close inspection of active sites in catalyst during the transition state in order to understand the mechanism behind it. It has certainly proven useful in explaining and understanding the accuracy of data collected. 
References:
<references />

Rep:Mod:qwt11

2014-01-30T23:09:21Z

Mh2710: /* Conformational analysis using Molecular Mechanics */

Experiment 1C: Organic Computational Lab

'''
== The Hydrogenation of Cyclopentadiene Dimer ==

'''Kinetic control VS Thermodynamic control'''

<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>1 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 1<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>2 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 2
<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>3 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 3
<jmol><jmolApplet><title>exo</title><color>white</color>
<size>200</size><script>measure 5 8 22;zoom 150; cpk -20;</script>
<uploadedFileContents>4 mol.mol</uploadedFileContents>
</jmolApplet></jmol>Dimer 4

Cyclopentadiene dimerises to an endo dimer and an exo dimer, 1&2. Hydrogenation of these two dimers proceeds to give two relative derivatives 3&4. The aim is to distinguish which product undergoes a thermodynamic or a kinetic reaction. A series of chemical related tools are used. “Chembio3D” shows both planar and stereo versions of molecules. "Gaussview" uses to display predicted NMR spectra. Under the help of “Avogadro”, a few types of crucial energy obtain, such as total bond stretching energy, total angle bending energy, total stretch bending energy, total torsional energy, total out-of-plane bending energy, total Van der Waals energy, total electrostatic energy and total energy (sum) of a particular. These information are allocated and the table below lists them out.

{| class="wikitable" border="1"
|+ Comparison of the results
! Property !! Dimer 1 (kcal/mol)!! Dimer 2 (kcal/mol) !! Dimer 3 (kcal/mol) !! Dimer 4 (kcal/mol)
|-
| Total bond stretching energy || 3.54360 || 3.46789 || 3.31086 || 2.93009
|-
| Total angle bending energy || 30.77335 ||33.18937 || 31.92713 || 21.09197
|-
| Total stretch bending energy || -2.04136 || -2.08218 || -2.10106 || -1.70918
|-
| Total torsional energy || -2.73744 || -2.94947 || -1.46254 || 0.17128
|-
| Total out-of-plane bending energy || 0.01469 || 0.02183 || 0.01315 || 0.00051
|-
| Total Van der Waals energy || 12.80707 || 12.35873 || 13.63924 || 10.68113
|-

| Total electrostatic energy || 13.01379 || 14.18450 || 5.11948 || 5.14891
|-
| Total energy || 55.37368 || 58.19067 || 50.44627 || 38.31470
|}

[[image:1234hydrogenation.png|thumb|left|470x470px|Hydrogenation of Cyclopentadiene]]

According to the table above, we clearly see that total energy (55.37368kcal/mol) of dimer 2 (55.37368kcal/mol) stays below while compare with dimer 1, which means dimer 1 is thermodynamic stable (ie: product stability) and dimer 2 is kinetic stable (ie: transition state stability). Likewise hydrogenated compound 3 gains more stability when it acts as a transition state and compound 4 prefers to act as a product. On the other hand, two indicated hydrogens senses more steric effect by the double bond in molecule 3, hence the higher total energy and less stable.

== Spectroscopic Simulation using Quantum Mechanics ==
'''
The NMR spectra of molecules can also be predicted by using Quantum Mechanics. These calculated results can then be compared with the chemical shifts reported in literature to investigate their accuracies. 

Molecule (17) is a derivative of taxol intermediate (9) found in the synthesis of Taxol. The 1H and 13C NMR spectra were computed and analysed below. 

<center>[[File:Qwt_molecule_17A.png‎|200px|]] 
'''Figure 2.1''': Molecule (17)</center> 

<center>[[File:17-1H_NMR.svg|800px|]] 
'''Figure 2.2''': 1H NMR spectrum of molecule (17) 

[[File:Molecule_17_-_protons.png|500px|]] 
'''Figure 2.3''': Labelled protons of molecule (17) 

[[File:1H NMR - 17.png|600px|]]
Table 2.1: Table illustrating the calculated shifts for 1H NMR of molecule (17) </center> 

The chemical shifts in the 1H NMR spectrum produced using Gaussian deviates from the literature<ref name="ja00398a003">LW. F. Maier and P. von Rague Schleyer, Journal of the American Chemistry Society, 1981, 103, 1891–1900. {{DOI|10.1021/ja00398a003}}</ref> by ~0.20-0.30 ppm, which is insignificant. An anomaly occurs for atoms #24, 48 and 51, which are expected to show a singlet in the NMR but are given their respective chemical shifts when computated. On close inspection of the respective protons, it was found that they were of different environments and should not have identical chemical shifts, implying an error in the reported results. In addition, the literature also poorly reported the peaks for atoms #19, 21-23, 26-31,33, 34, 49 and 51 as multiplets whereas they are given individual chemical shifts when computated. Given that the results were produced 23 years ago, where NMR techniques were not as advanced, such observation are expected. Hence the computed results are clearly more accurate. 

<center>[[File:17-13C_NMR.svg|800px|]] 
'''Figure 2.4''': 13C NMR spectrum of molecule (17) 

[[File:Molecule_17_-_carbons.png|500px|]] 
'''Figure 2.5''': Labelled carbons of molecule (17) 

[[File:13C NMR - 17.png|500px|]] <
Table 2.2: Table illustrating the calculated shifts for 13C NMR of molecule (17)</center> 

The chemical shifts in the 13C NMR spectrum produced using Gaussian are similar to the ones reported in the literature. The greatest deviation is observed for atom #14. This is because the Carbon atom is adjacent to 2 Sulfur atoms, which are considered to be heavy atoms, and correction to the chemical shift needs to be made to remove the spin-orbit coupling error. 

The thermodynamic quantities of molecule (17) were also computed and listed below:

<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" | Types of energies
! style="background: #fdb813; color: black;" |Energies(Hartree/Particle)
|-
| Zero-point correction
| style="text-align: center;" |0.468397
|-
| Thermal correction to Energy
| style="text-align: center;" |0.489751
|-
| Thermal correction to Enthalpy
| style="text-align: center;" |0.490696
|-
| Thermal correction to Gibbs Free Energy
| style="text-align: center;" |0.422010
|-
| Sum of electronic and zero-point Energies
| style="text-align: center;" |-1651.414384
|-
| Sum of electronic and thermal Energies
| style="text-align: center;" |-1651.393029
|-
| Sum of electronic and thermal Enthalpies
| style="text-align: center;" |-1651.392085
|-
| Sum of electronic and thermal Free Energies
| style="text-align: center;" |-1651.460770
|}
</center>
<center>Table 2.3: Thermodynamic quantities of molecule (17)</center> 

From Table 2.3, ΔG is calculated to be -1650kcal/mol. This value can be compared with the ΔG of molecule (18) to determine which molecule is more stable at room temperature.
 
References:
<references />
 

== '''Analysis of the properties of the synthesised alkene epoxides''' ==

(I) Catalyst Structures 
The stable precursor (21) of the Shi catalyst shown below was synthesised for the epoxidation of styrene and trans-B-methyltyrene.

<center>[[File:Molecule_21_sticks.png|350px|]] 
'''Figure 3.1''': Molecule 21 with labelled bond lengths and angles</center> 

<center>[[File:Molecule_21.png|400px|]] 
'''Figure 3.2''': Stick diagram of molecule 21 with the C-O bond lengths</center> 

Close examination of the C-O bond lengths in the anomeric centres with O-C-O substructures found that one C-O bond is significantly longer than the other. This is presented in Figure 3.2, where the bottom anomeric centre shows C-O bond lengths of 1.428Å and 1.456Å, when the expected bond length is 1.43Å. This is similarly found in the top anomeric structure. In addition, the terminal methyl groups are found to have shorter than normal C-C bonds (1.54Å) with values ranging from 1.500Å - 1.511Å. This observation is likely due to overlap of the p* orbitals in O atoms that have weak C-O bonds and the sp3 orbitals in C atoms. As a result the bonding orbitals of the C atoms are stabilised, resulting in stronger C-C bonds while the donation of some electron density to the p* orbital due to the overlap decreases the bond order and weakens the C-O bond. The O-C-O angles are also observed to be smaller than the expected value of 109.5o. The anomeric centre that is contained in both the 5-membered ring and 6-membered ring has shorter than normal C-O bonds with values of 1.415Å and 1.423Å. The short C-O bond can be explained by the resonance effect to the nearby C=O group. 

For the Jacobsen asymmetric catalyst, the stable pre-catalyst (23) formed in the reaction is shown below. 

<center>[[File:Molecule2301.png|250px|]] 
'''Figure 3.3''': Molecule 23</center> 

<center>[[File:Molecule_23_stick_and_ball.png|350px|]] 
'''Figure 3.4''': Sticks and ball diagram of molecule 23</center> 

Referring to Figure 3.4, a close approach of the 2 adjacent t-butyl groups on the rings is observed. When the shortest distance between the protons were measured, it was found to be 2.421Å, which corresponds to the Van Der Waals radii for the maximum attractive interaction<ref name="conformationalanalysis">H. S. Rzepa, 2010.</ref>. This helps to stabilise the molecule strongly. The dominance of the strong H...H Van Der Waals interactions is further supported by the fact that it is present despite the close proximity that results in repulsive O..H Van der Waals interactions (2.335Å and 2.193Å) being observed too. 

The rest of the report will be based on the (R) and (S) styrene oxides and the (R)(R), (S)(S), (R)(S), (S)(R) trans-ß-Methylstyrene oxides.

(II) NMR of selected epoxides 
The NMR spectra of the selected epoxides were computed and the calculated chemical shifts were compared with those found in literature as no NMR spectra of the epoxides were produced in the actual synthesis. 
 
(R)-Styrene oxide 
The (S)-Styrene oxide produces the same NMR data as the (R)-Styrene oxide and will not be shown below. 
<center>[[File:R_Styrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.1''': Labelled atoms of (R)-Styrene oxide 

[[File:R_Styrene_oxide_NMR_1H.svg|800px|]] 
'''Figure 4.2''': 1H NMR spectrum of (R)-Styrene oxide 

[[File:R_Styrene_oxide_1H_NMR_table.png|500px|]]
Table 3.1: Table illustrating the calculated shifts for 1H NMR of (R)-Styrene oxide<ref name="j.tetasy.2009.005.001">K. Sarma, A. Goswamia, and B. C. Goswamib, Tetrahedron, 2009, 20, 1295–1300.{{DOI|10.1016/j.tetasy.2009.005.001}}</ref> </center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="j.tetasy.2009.005.001" /> with insignificant derivations of <0.20ppm. Precision is seen in the calculated values which indicate that proton #13 has a different chemical shift than the rest of the protons. This is likely due to the close proximity of proton #13 with the O atom. However, protons #11 and #14 should not have the same chemical shift as protons #10 and #12 as they are not chemically equivalent. 

<center>[[File:R_Styrene_oxide_NMR_13C.svg|800px|]] 
'''Figure 4.3''': 13C NMR spectrum of (R)-Styrene oxide 

[[File:R_Styrene_oxide_13C_NMR_table.png|500px|]]
Table 3.2: Table illustrating the calculated shifts for 13C NMR of (R)-Styrene oxide<ref name="j.tetasy.2009.005.001" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="j.tetasy.2009.005.001" /> with insignificant derivations of <5.00ppm. The literature failed to report 2 of the chemical shifts for the protons, likely due to its close proximity on the spectra that results in overlaps. 

(R),(R)-trans-ß-Methylstyrene oxide 
The (S),(S)-trans-ß-Methylstyrene oxide produces the same NMR data as the (R),(R)-trans-ß-Methylstyrene oxide and will not be shown below. 
<center>[[File:2R,3R-trans-ß-Methylstyrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.4''': Labelled atoms of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_1H_NMR.svg|800px|]] 
'''Figure 4.5''': 1H NMR spectrum of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_1H_NMR_table.png|500px|]]
Table 3.3: Table illustrating the calculated shifts for 1H NMR of (R),(R)-trans-ß-Methylstyrene oxide<ref name="jo900739q">O. Andrea Wong, B. Wang, M.-X. Zhao, and Y. Shi, Journal of Organic Chemistry , 2009, 74, 6335–6338.{{DOI|10.1021/jo900739q}}</ref></center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="jo900739q" />. Protons #18-20 were reported to have 3 different chemical shifts despite belonging to a -CH3 group. This indicates that the computed results took into account that presence of slow rotation about the C atom due to the hindrance of the O atom which results in the 3 protons being seen as having different environments. Additionally, the aromatic proton #15 does not have the same chemical shift as proton #14 despite being in the same chemical environment. This implies that they are magnetically inequivalent. This is possible if there's slow rotation about the C(Ph)-C(OC) bond. 

<center>[[File:2R,3R-trans-ß-Methylstyrene_oxide_13C_NMR.svg|800px|]] 
'''Figure 4.6''': 13C NMR spectrum of (R),(R)-trans-ß-Methylstyrene oxide 

[[File:2R,3R-trans-ß-Methylstyrene_oxide_13C_NMR_table.png|500px|]]
Table 3.4: Table illustrating the calculated shifts for 13C NMR of (R),(R)-trans-ß-Methylstyrene oxide<ref name="jo900739q" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="jo900739q" />. As seen previously, the computed results show individual chemical shifts for the aromatic carbons which is not seen in the literature. 

(R),(S)-trans-ß-Methylstyrene oxide 
The (S),(R)-trans-ß-Methylstyrene oxide produces the same NMR data as the (R),(S)-trans-ß-Methylstyrene oxide and will not be shown below. 
<center>[[File:2S,_3R-trans-ß-Methylstyrene_oxide_NMR_labelled.png|500px|]] 
'''Figure 4.7''': Labelled atoms of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_1H_NMR.svg|800px|]] 
'''Figure 4.8''': 1H NMR spectrum of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_1H_NMR_table.png|500px|]]
Table 3.5: Table illustrating the calculated shifts for 1H NMR of (R),(S)-trans-ß-Methylstyrene oxide<ref name="anie.201201848">S. Koya, Y. Nishioka, H. Mizoguchi, T. Uchida, and T. Katsuki, Angewandte Chemie International Edition, 2012, 51, 8243–8246.{{DOI|10.1002/anie.201201848}}</ref></center> 

The calculated 1H NMR chemical shifts are in line with the reported values<ref name="anie.201201848" />. The observation for (R),(R)-trans-ß-Methylstyrene oxide is also seen here; protons #11, 12 and 20 are found to be of different chemical shifts despite belonging to the same -CH3 group. Similarly, protons #15 and 19 are calculated to have different chemical shifts despite being chemically equivalent, implying that they are magnetically inequivalent. 

<center>[[File:2S,3R-trans-ß-Methylstyrene_oxide_13C_NMR.svg|800px|]] 
'''Figure 4.9''': 13C NMR spectrum of (R),(S)-trans-ß-Methylstyrene oxide 

[[File:2S,3R-trans-ß-Methylstyrene_oxide_13C_NMR_table.png|500px|]]
Table 3.6: Table illustrating the calculated shifts for 13C NMR of (R),(S)-trans-ß-Methylstyrene oxide<ref name="anie.201201848" /></center> 

The calculated 13C NMR chemical shifts are in line with the reported values<ref name="anie.201201848" />. As seen previously, the computed results show individual chemical shifts for the aromatic carbons which is not seen in the literature. 

(III) Calculated chiroptical properties of selected epoxides 
The optical rotation values were calculated for 3 different epoxides; their respective enantiomers were assumed to have the same values but of different signs. No comparison is made with experimental results as none were produced due to the lack of time, hence comparison is made with litera 

<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Epoxides
! style="background: #fdb813; color: black;" |Calculated values of [α]D (o)
! style="background: #fdb813; color: black;" |Reported values of [α]D (o)
|-
| (R)-Styrene Oxide
| style="text-align: center;" |-179.79
| style="text-align: center;" |-23.7<ref name="j.tetasy.2003.09.024">D. E. White and E. N. Jacobsen, Tetrahedron, 2003, 14, 3633–3638.{{DOI|10.1016/j.tetasy.2003.09.024}}</ref>
|-
| (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |+131.77
| style="text-align: center;" |+44.3<ref name="jo900739q" />
|-
| (S),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |+33.99
| style="text-align: center;" |+38.6<ref name="anie.201201848" />
|}
</center>
<center>Table 4.1: Table showing the epoxides and their calculated optical rotations</center> 
The calculated values of [α]D (o) all show the same sign as the ones reported. However, the computed value for (R)-Styrene oxide largely deviates from the literature value, with a difference of 157o. Similarly, the computed value for (R),(R)-trans-ß-Methylstyrene oxide also deviates from the literature by 87o. Only the computed value for (S),(R)-trans-ß-Methylstyrene oxide is close to the value reported. Since the specific optical rotation already takes into account the path length and the concentration of the molecules, the large deviation is likely due to the difference in conformations between the ones used for calculations and the ones done in experiment. This is because the computed values differ for different conformers of the same compound. At the same time, it is also possible that the deviation is due to presence of impurities during measurement in the experiment. This is because the epoxides are produced in a racemic mixture and separation is required before measuring the optical rotation. Hence it is difficult to evaluate the accuracy of the computed results and the literature results as different literature reports produce different values too. One way of improving the computed results will be to repeatedly produce optimised molecules for computation. 

 
(IV) Using the properties of transition state for the reaction 
Shi catalyst transition states 
Trans-ß-Methylstyrene oxide and styrene oxide were chosen for this segment. 

Out of the 8 transition states provided for the (R),(R)-trans-ß-Methylstyrene oxide and the (S),(S)-trans-ß-Methylstyrene oxide, the ones with the lowest energies, i.e. largest magnitude since G<0, were chosen for further calculations. This is because the lowest energies transition states are the most stable and will most likely occur to give the epoxides. The values obtained from the .log files were also converted from Hartree/particle to Joules/mol.

<center>
{| class="wikitable"
| G of (R),(R)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-1343.032443
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-1343.024742
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-3.5261343E+09
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-3.5261341E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.02E+04
|-
| K ([(R),(R) enatiomer]/[(S),(S) enantiomer])
| style="text-align: center;" |3485.09
|-
| Ratio of (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |0.9997
|-
| Ratio of (S),(S)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |2.869E-04
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.9
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |96-98<ref name="Shi01">Z.-X. Wang, L. Shu, M. Frohn, Y. Tu, and Y. Shi, Organic Syntheses, 2003, 80, 9.</ref>
|}
</center>
<center>Table 5.1: Table showing calculations for the transition states for the epoxidation of trans-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.02E+04 Joules/mol, implying that (R),(R)-trans-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (R),(R)-trans-ß-Methylstyrene oxide over (S),(S)-trans-ß-Methylstyrene oxide is denoted as K and given to be 3485.09. Since the ratio of both concentrations add up to 1, the predicted enantiomer excess is calculated to be 99.9% with the (R),(R)-trans-ß-Methylstyrene oxide being the dominating enantiomer. This is in line with the reported value of 96-98% by Shi<ref name="Shi01" /> 

<center>
{| class="wikitable"
| G of (R)-styrene oxide (Hartree/Particle)
| style="text-align: center;" |-1303.738044
|-
| G of (S)-styrene oxide (Hartree/Particle)
| style="text-align: center;" |-1303.738503
|-
| G of (R)-styrene oxide (Joules/mol)
| style="text-align: center;" |-3.422967E+09
|-
| G of (S)-styrene oxide (Joules/mol)
| style="text-align: center;" |-3.422968E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |1.21E+04
|-
| K ([(R) enantiomer]/[(S) enatiomer])
| style="text-align: center;" |0.615
|-
| Ratio of (R)-styrene oxide
| style="text-align: center;" |0.619
|-
| Ratio of (S)-styrene oxide
| style="text-align: center;" |0.381
|-
| Enantiomeric excess (%)
| style="text-align: center;" |23.8
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |24.3<ref name="Shi02">Z.-X. Wang, Y. Tu, M. Frohn, J.-R. Zhang, and Y. Shi, Journal of the American Chemistry Society, 1997, 119, 11224–11235.{{DOI|10.1021/ja972272g}}</ref>
|}
</center>
<center>Table 5.2: Table showing calculations for the transition states for the epoxidation of styrene </center> 
The difference in free energies (∆G) is calculated to be 1.21E+04 Joules/mol, implying that (S)-styrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (R)-styrene oxide over (S)-styrene oxide is denoted as K and given to be 0.615. The predicted enantiomer excess is calculated to be 23.8% with the (R)-styrene oxide being the dominating enantiomer. This is also in line with the reported value of 24.3% by Shi<ref name="Shi02" />. 

Jacobsen catalyst transition states 
<center>
{| class="wikitable"
| G of (S),(R)-cis-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.259559
|-
| G of (R),(S)-cis-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.25106
|-
| G of (S),(R)-cis-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88275E+09
|-
| G of (R),(S)-cis-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88273E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.23E+04
|-
| K ([(S),(R)enantiomer]/[(R),(S) enantiomer])
| style="text-align: center;" |8114.63
|-
| Ratio of (S),(R)-cis-ß-Methylstyrene oxide
| style="text-align: center;" |1.23E-04
|-
| Ratio of (R),(S)-cis-ß-Methylstyrene oxide
| style="text-align: center;" |0.9999
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.9%
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |92<ref name="ja00018a068">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. , Ecker, and L. Deng, Journal of the American Chemistry Society, 1991, 113, 7063–7064.{{DOI|10.1021/ja00018a068}}</ref>
|}
</center>
<center>Table 5.3: Table showing calculations for the transition states for the epoxidation of cis-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.23E+04 Joules/mol, implying that (S),(R)-cis-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of (S),(R)-cis-ß-Methylstyrene oxide over (R),(S)-cis-ß-Methylstyrene oxide is denoted as K and given to be 8114.63. The predicted enantiomer excess is calculated to be 99.9% with the (R),(S)-cis-ß-Methylstyrene oxide being the dominating enantiomer. This is slightly higher than the experimental results by Jacobsen<ref name="ja00018a068" /> but it still ties in with the observation that the (R),(S)-cis-ß-Methylstyrene oxide is preferentially formed. 

<center>
{| class="wikitable"
| G of (S),(S)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.262481
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Hartree/Particle)
| style="text-align: center;" |-3383.254344
|-
| G of (S),(S)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88276E+09
|-
| G of (R),(R)-trans-ß-Methylstyrene oxide (Joules/mol)
| style="text-align: center;" |-8.88274E+09
|-
| ∆G (Joules/mol)
| style="text-align: center;" |-2.14E+04
|-
| K ([(S),(S)enantiomer]/[(R),(R) enantiomer])
| style="text-align: center;" |5530.45
|-
| Ratio of (S),(S)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |0.9998
|-
| Ratio of (R),(R)-trans-ß-Methylstyrene oxide
| style="text-align: center;" |1.81E-04
|-
| Enantiomeric excess (%)
| style="text-align: center;" |99.96
|-
| Reported enantiomeric excess (%)
| style="text-align: center;" |92<ref name="ol0069406">A. M. Daly, M. F. Renehan, and D. G. Gilheany, Organic Letters, 2001, 3, 663–666.{{DOI|10.1021/ol0069406}}</ref>
|}
</center>
<center>Table 5.4: Table showing calculations for the transition states for the epoxidation of trans-ß-Methylstyrene </center> 
The difference in free energies (∆G) is calculated to be -2.14E+04 Joules/mol, implying that S),(S)-trans-ß-Methylstyrene oxide has a more stable transition state. Given that ∆G =-RTlnK, where R is the gas constant(8.314JK-1mo-1) and T is the temperature(298.15K). The ratio of concentrations of S),(S)-trans-ß-Methylstyrene oxide over (R),(R)-trans-ß-Methylstyrene oxide is denoted as K and given to be 5530.45. The predicted enantiomer excess is calculated to be 99.96% with the (S),(S)-trans-ß-Methylstyrene oxide being the dominating enantiomer. This is slightly higher than the literature value of 92% but the preference for the formation of (S),(S)-trans-ß-Methylstyrene oxide is supported. 

(V) Investigating the non-covalent interactions in the active-site of the reaction transition state 
 The (R),(R)-trans-ß-Methylstyrene oxide transition state using the Shi catalyst is chosen for this analysis. 

<center>[[File:RRNCIfile.png|500px|]] 
'''Figure 5.1''': NCI analysis of the transition state using Shi catalyst to form (R),(R)-trans-ß-Methylstyrene oxide </center>
 
It can be observed that active site in the Shi catalyst is positioned at one of the dioixirane O atoms. Observation of blue and green electron density near the active site indicates very attractive interaction between the catalyst and the alkene at this position. Specifically, the 5-membered ring on the Shi catalyst shows strong interaction with the protons on the methyl group and the phenyl ring which are positioned closely to the alkene functional group such that they enclose it. In addition, the dioxirane O atom that is not involved in the epoxidation shows hydrogen bond like interaction with a proton on the protruding methyl group at the other end. Intramolecular hydrogen bonding interaction is also observed in the Shi catalyst between the proton on the methyl group and ether O in the 6-membered ring. These attractive interactions help to stabilise the overall system and are a result of an endo-type interaction between the dioxirane O atom and the alkene functional group where the latter is positioned directly above the former. As a result, the epoxidation of the trans-ß-Methylstyrene is a syn addition to the alkene double bond. This explains the formation of the (R),(R)-trans-ß-Methylstyrene oxide enantiomer from this transition state.
 
(VI) Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state 
The electronic topology of the transition state for the formation of (R),(R)-trans-ß-Methylstyrene oxide using Shi catalyst is shown below.
 
<center>[[File:(RR)QTAIM.png|500px|]] 

'''Figure 6.1''': Electronic topology of the transition state using Shi catalyst to form (R),(R)-trans-ß-Methylstyrene oxide </center> 
Atoms that are involved in weak non-covalent bond critical point(BCP) are annotated in Figure 6.1. On close inspection, it is observed that there is an absence of a bond (i.e. BCP not seen) between the dioxirane O atoms in the Shi catalyst. With the lack of a covalent bond, the O atom that is not involved in the epoxidation is stabilised by hydrogen bonding with a proton on the methyl group as it has the most suitable distance for attractive interaction. On the other hand, the O atom involved in epoxidation is stabilised by weak non-covalent interactions with the C atom on the alkene C=C that is less hindered. This illustrates the means of epoxidation. In additional, the overall structure is stablised by favourable weak interactions such as hydrogen bonding between the O atom in the 5-membered ring with suitable H atoms and H...H Van Der Waals interactions.
 

(VII) Suggesting new candidates for investigations 
One alkene that can be epoxidised to give an epoxide with [α]D=835.9o<ref name="jo01045a016">W. Reusch and C. K. Johnson, Journal of Organic Chemistry, 1963, 28, 2557–2560.{{DOI|10.1021/jo01045a016}}</ref> is (+)-pulegone shown below: 
<center>[[File:D-pulegone.png|350px|]] 
'''Figure 7.1''': Epoxidation of (+)-pulegone </center> 
This will give cis R-(+)-pulegone oxide. 

Conclusion 
In conclusion, the use of computational methods has allowed an expansion on the experiment performed for the epoxidation of selected alkenes using Shi catalyst and Jacobsen catalyst. It has proven useful in conformational analysis of specific compounds to explain unexpected observations seen in experiments. Similarly, it also allows the computation of NMR spectra of various optimised molecules which can then be compared with the ones produced in literature. More importantly, it helps to calculate free energies which is use to identify the stability of the molecules. Optical rotation of chiral epoxides were also computed but more can be expanded in this area to ensure its accuracy. Computational methods also allow close inspection of active sites in catalyst during the transition state in order to understand the mechanism behind it. It has certainly proven useful in explaining and understanding the accuracy of data collected. 
References:
<references />

Rep:Mod:mh2710tata2

2013-03-15T17:00:38Z

Mh2710: /* (a) Optimisation of guess transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:59:46Z

Mh2710: /* Reoptimisation of boat transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:59:22Z

Mh2710: /* Reoptimisation of chair transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:58:51Z

Mh2710: /* IRC analysis of optimised boat transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:58:17Z

Mh2710: /* IRC analysis of optimised chair transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:57:37Z

Mh2710: /* Second optimisation from modified reactant and product */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:56:36Z

Mh2710: /* First optimisation from optimised anti2 1,5-hexadiene */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The correct boat structure was not obtained from the QST2 method . Hence the structure shown below which looks a bit like the chair transition state was used instead.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:54:19Z

Mh2710: /* (d) Reoptimisation of chair transition state with unfrozen coordinates */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The optimised bond distance of transition state using the redundant coordinate editor is just slightly lower than that of using computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:51:41Z

Mh2710: /* (d) Reoptimisation of chair transition state with unfrozen coordinates */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:50:45Z

Mh2710: /* (c) Optimisation of chair transition state using frozen coordinate method */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]

The bond distance between the terminal C atoms of the allyl fragments is fixed to 2.2 Å.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:47:31Z

Mh2710: /* Discussion */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state. There is node between butadiene and anhydride fragment in exo transition state hence there is no interaction between them.

Rep:Mod:mh2710tata2

2013-03-15T16:43:12Z

Mh2710: /* Discussion */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

The activation energy of exo transition state is 27.26281829 kcal/mol, which is higher than that of endo transition state(26.58200131 kcal/mol). Hence endo transition state is more stable than the exo one leading to major product being endo. This is because secondary orbital overlap effects- the HOMO of the butadiene fragment has the right phase to interact with LUMO of the anhydride fragment, stabilising the endo transition state.

Rep:Mod:mh2710tata2

2013-03-15T16:25:44Z

Mh2710: /* (b) Optimisation of chair transition state by computing force constants */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====

Two optimised allyl fragments were combined and modified to have a conformation very close to a chair transition state.

'''1. Optimising chair transition state using Berny method with force constants calculation'''

 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''

 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''

 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''

 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

[[File:mh-allyl-chair-opt-freq.gif]]

From the table above, only one imaginary frequency that has a magnitude of 817.99 cm-1. It's vibration animation shows there are 2 carbon atoms coming closer at the same time indicating a concerted bond formation and there are 2 carbon atoms leaving far away at the same time indicating a synchronous bond breaking.

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

Rep:Mod:mh2710tata2

2013-03-15T16:13:47Z

Mh2710: /* (a) Optimisation of allyl fragment */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====

An allyl fragment was drawn and optimised for further use.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

Rep:Mod:mh2710tata2

2013-03-15T16:10:36Z

Mh2710: /* (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====

A better basis set i.e. B3LYP/6-31G(d) was used to reoptimise the anti2 conformer in order to get higher accuracy.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''

 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.

[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]

{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}

From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

Rep:Mod:mh2710tata2

2013-03-15T16:04:33Z

Mh2710: /* Optimising the Exo and Endo Transition Structures */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

===== Discussion =====

Rep:Mod:mh2710tata2

2013-03-15T15:59:12Z

Mh2710: /* (a) Optimisation of guess transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.22 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:45:33Z

Mh2710: /* Discussion */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

The table above shows literature values of different C-C bond lengths. The bond length calculated from optimisation of transition state is shorter than two van der Waals radii which shows attractive forces between terminal carbons of cis-Butadiene and ethylene. In addition, the bond distanced is much larger than any of the literature values, indicating the bond is only partly formed.

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:32:45Z

Mh2710: /* Discussion */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

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

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:31:33Z

Mh2710: /* Optimising the Transition Structure */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== Discussion =====

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:30:31Z

Mh2710: /* (c) Reoptimisation of transition state using B3LYP/6-31G(d) */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:28:51Z

Mh2710: /* (a) Optimisation of guess transition state */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11926 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== (c) Reoptimisation of transition state using B3LYP/6-31G(d) =====
'''1. Optimising transition state using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DA TS OPT BERNY AM1 631GD.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:DA TS OPT BERNY AM1 631GD.LOG| here]].

'''3. General information'''
 
[[File:DA TS OPT BERNY AM1 631gd info.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000496 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
Predicted change in Energy=-7.705534D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.386 -DE/DX = 0.0 !
! R2 R(1,6) 2.9004 -DE/DX = 0.0 !
! R3 R(1,7) 2.2725 -DE/DX = 0.0 !
! R4 R(1,9) 2.7536 -DE/DX = 0.0 !
! R5 R(1,10) 2.4251 -DE/DX = 0.0 !
! R6 R(1,15) 1.0842 -DE/DX = 0.0 !
! R7 R(1,16) 1.0863 -DE/DX = 0.0 !
! R8 R(2,3) 2.2725 -DE/DX = 0.0 !
! R9 R(2,4) 2.9004 -DE/DX = 0.0 !
! R10 R(2,11) 2.4251 -DE/DX = 0.0 !
! R11 R(2,12) 2.7536 -DE/DX = 0.0 !
! R12 R(2,13) 1.0842 -DE/DX = 0.0 !
! R13 R(2,14) 1.0863 -DE/DX = 0.0 !
! R14 R(3,4) 1.383 -DE/DX = 0.0 !
! R15 R(3,11) 1.084 -DE/DX = 0.0 !
! R16 R(3,12) 1.0873 -DE/DX = 0.0 !
! R17 R(3,13) 2.5399 -DE/DX = 0.0 !
! R18 R(3,14) 2.5323 -DE/DX = 0.0 !
! R19 R(4,5) 1.0891 -DE/DX = 0.0 !
! R20 R(4,6) 1.4072 -DE/DX = 0.0 !
! R21 R(6,7) 1.383 -DE/DX = 0.0 !
! R22 R(6,8) 1.0891 -DE/DX = 0.0 !
! R23 R(7,9) 1.0873 -DE/DX = 0.0 !
! R24 R(7,10) 1.084 -DE/DX = 0.0 !
! R25 R(7,15) 2.5399 -DE/DX = 0.0 !
! R26 R(7,16) 2.5323 -DE/DX = 0.0 !
! A1 A(2,1,6) 90.2098 -DE/DX = 0.0 !
! A2 A(2,1,7) 109.1164 -DE/DX = 0.0 !
! A3 A(2,1,9) 131.4998 -DE/DX = 0.0 !
! A4 A(2,1,10) 98.9089 -DE/DX = 0.0 !
! A5 A(2,1,15) 120.0522 -DE/DX = 0.0 !
! A6 A(2,1,16) 119.9852 -DE/DX = 0.0 !
! A7 A(6,1,9) 44.4899 -DE/DX = 0.0 !
! A8 A(6,1,10) 46.5393 -DE/DX = 0.0 !
! A9 A(6,1,15) 83.3596 -DE/DX = 0.0 !
! A10 A(6,1,16) 118.2474 -DE/DX = 0.0 !
! A11 A(9,1,10) 40.6754 -DE/DX = 0.0 !
! A12 A(9,1,15) 77.8409 -DE/DX = 0.0 !
! A13 A(9,1,16) 80.5628 -DE/DX = 0.0 !
! A14 A(10,1,15) 116.9474 -DE/DX = 0.0 !
! A15 A(10,1,16) 74.6439 -DE/DX = 0.0 !
! A16 A(15,1,16) 115.1638 -DE/DX = 0.0 !
! A17 A(1,2,3) 109.1165 -DE/DX = 0.0 !
! A18 A(1,2,4) 90.2099 -DE/DX = 0.0 !
! A19 A(1,2,11) 98.9089 -DE/DX = 0.0 !
! A20 A(1,2,12) 131.5 -DE/DX = 0.0 !
! A21 A(1,2,13) 120.0522 -DE/DX = 0.0 !
! A22 A(1,2,14) 119.9852 -DE/DX = 0.0 !
! A23 A(4,2,11) 46.5393 -DE/DX = 0.0 !
! A24 A(4,2,12) 44.49 -DE/DX = 0.0 !
! A25 A(4,2,13) 83.3596 -DE/DX = 0.0 !
! A26 A(4,2,14) 118.2474 -DE/DX = 0.0 !
! A27 A(11,2,12) 40.6755 -DE/DX = 0.0 !
! A28 A(11,2,13) 116.9475 -DE/DX = 0.0 !
! A29 A(11,2,14) 74.644 -DE/DX = 0.0 !
! A30 A(12,2,13) 77.8409 -DE/DX = 0.0 !
! A31 A(12,2,14) 80.5627 -DE/DX = 0.0 !
! A32 A(13,2,14) 115.1638 -DE/DX = 0.0 !
! A33 A(4,3,11) 120.6613 -DE/DX = 0.0 !
! A34 A(4,3,12) 120.0232 -DE/DX = 0.0 !
! A35 A(4,3,13) 94.0558 -DE/DX = 0.0 !
! A36 A(4,3,14) 127.3507 -DE/DX = 0.0 !
! A37 A(11,3,12) 114.4864 -DE/DX = 0.0 !
! A38 A(11,3,13) 109.2312 -DE/DX = 0.0 !
! A39 A(11,3,14) 69.5135 -DE/DX = 0.0 !
! A40 A(12,3,13) 88.6205 -DE/DX = 0.0 !
! A41 A(12,3,14) 91.9441 -DE/DX = 0.0 !
! A42 A(13,3,14) 42.3516 -DE/DX = 0.0 !
! A43 A(2,4,5) 121.3465 -DE/DX = 0.0 !
! A44 A(2,4,6) 89.7903 -DE/DX = 0.0 !
! A45 A(3,4,5) 118.6679 -DE/DX = 0.0 !
! A46 A(3,4,6) 122.0341 -DE/DX = 0.0 !
! A47 A(5,4,6) 117.9096 -DE/DX = 0.0 !
! A48 A(1,6,4) 89.7901 -DE/DX = 0.0 !
! A49 A(1,6,8) 121.3467 -DE/DX = 0.0 !
! A50 A(4,6,7) 122.0341 -DE/DX = 0.0 !
! A51 A(4,6,8) 117.9096 -DE/DX = 0.0 !
! A52 A(7,6,8) 118.6679 -DE/DX = 0.0 !
! A53 A(6,7,9) 120.0232 -DE/DX = 0.0 !
! A54 A(6,7,10) 120.6613 -DE/DX = 0.0 !
! A55 A(6,7,15) 94.0558 -DE/DX = 0.0 !
! A56 A(6,7,16) 127.3506 -DE/DX = 0.0 !
! A57 A(9,7,10) 114.4864 -DE/DX = 0.0 !
! A58 A(9,7,15) 88.6207 -DE/DX = 0.0 !
! A59 A(9,7,16) 91.9443 -DE/DX = 0.0 !
! A60 A(10,7,15) 109.2309 -DE/DX = 0.0 !
! A61 A(10,7,16) 69.5133 -DE/DX = 0.0 !
! A62 A(15,7,16) 42.3515 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -20.742 -DE/DX = 0.0 !
! D2 D(6,1,2,4) 0.0 -DE/DX = 0.0 !
! D3 D(6,1,2,11) -45.918 -DE/DX = 0.0 !
! D4 D(6,1,2,12) -18.3309 -DE/DX = 0.0 !
! D5 D(6,1,2,13) 82.445 -DE/DX = 0.0 !
! D6 D(6,1,2,14) -123.2664 -DE/DX = 0.0 !
! D7 D(7,1,2,3) -0.0001 -DE/DX = 0.0 !
! D8 D(7,1,2,4) 20.742 -DE/DX = 0.0 !
! D9 D(7,1,2,11) -25.1761 -DE/DX = 0.0 !
! D10 D(7,1,2,12) 2.4111 -DE/DX = 0.0 !
! D11 D(7,1,2,13) 103.1869 -DE/DX = 0.0 !
! D12 D(7,1,2,14) -102.5244 -DE/DX = 0.0 !
! D13 D(9,1,2,3) -2.4112 -DE/DX = 0.0 !
! D14 D(9,1,2,4) 18.3308 -DE/DX = 0.0 !
! D15 D(9,1,2,11) -27.5872 -DE/DX = 0.0 !
! D16 D(9,1,2,12) -0.0001 -DE/DX = 0.0 !
! D17 D(9,1,2,13) 100.7758 -DE/DX = 0.0 !
! D18 D(9,1,2,14) -104.9356 -DE/DX = 0.0 !
! D19 D(10,1,2,3) 25.176 -DE/DX = 0.0 !
! D20 D(10,1,2,4) 45.918 -DE/DX = 0.0 !
! D21 D(10,1,2,11) -0.0001 -DE/DX = 0.0 !
! D22 D(10,1,2,12) 27.5871 -DE/DX = 0.0 !
! D23 D(10,1,2,13) 128.3629 -DE/DX = 0.0 !
! D24 D(10,1,2,14) -77.3484 -DE/DX = 0.0 !
! D25 D(15,1,2,3) -103.1869 -DE/DX = 0.0 !
! D26 D(15,1,2,4) -82.4449 -DE/DX = 0.0 !
! D27 D(15,1,2,11) -128.3629 -DE/DX = 0.0 !
! D28 D(15,1,2,12) -100.7758 -DE/DX = 0.0 !
! D29 D(15,1,2,13) 0.0 -DE/DX = 0.0 !
! D30 D(15,1,2,14) 154.2887 -DE/DX = 0.0 !
! D31 D(16,1,2,3) 102.5243 -DE/DX = 0.0 !
! D32 D(16,1,2,4) 123.2663 -DE/DX = 0.0 !
! D33 D(16,1,2,11) 77.3483 -DE/DX = 0.0 !
! D34 D(16,1,2,12) 104.9354 -DE/DX = 0.0 !
! D35 D(16,1,2,13) -154.2888 -DE/DX = 0.0 !
! D36 D(16,1,2,14) -0.0001 -DE/DX = 0.0 !
! D37 D(2,1,6,4) 0.0 -DE/DX = 0.0 !
! D38 D(2,1,6,8) -123.0828 -DE/DX = 0.0 !
! D39 D(9,1,6,4) -160.3592 -DE/DX = 0.0 !
! D40 D(9,1,6,8) 76.5581 -DE/DX = 0.0 !
! D41 D(10,1,6,4) -102.1158 -DE/DX = 0.0 !
! D42 D(10,1,6,8) 134.8014 -DE/DX = 0.0 !
! D43 D(15,1,6,4) 120.2482 -DE/DX = 0.0 !
! D44 D(15,1,6,8) -2.8345 -DE/DX = 0.0 !
! D45 D(16,1,6,4) -124.7021 -DE/DX = 0.0 !
! D46 D(16,1,6,8) 112.2151 -DE/DX = 0.0 !
! D47 D(1,2,4,5) 123.0828 -DE/DX = 0.0 !
! D48 D(1,2,4,6) 0.0 -DE/DX = 0.0 !
! D49 D(11,2,4,5) -134.8015 -DE/DX = 0.0 !
! D50 D(11,2,4,6) 102.1157 -DE/DX = 0.0 !
! D51 D(12,2,4,5) -76.5581 -DE/DX = 0.0 !
! D52 D(12,2,4,6) 160.3591 -DE/DX = 0.0 !
! D53 D(13,2,4,5) 2.8345 -DE/DX = 0.0 !
! D54 D(13,2,4,6) -120.2482 -DE/DX = 0.0 !
! D55 D(14,2,4,5) -112.2151 -DE/DX = 0.0 !
! D56 D(14,2,4,6) 124.7022 -DE/DX = 0.0 !
! D57 D(11,3,4,5) -160.592 -DE/DX = 0.0 !
! D58 D(11,3,4,6) 33.1448 -DE/DX = 0.0 !
! D59 D(12,3,4,5) -6.5509 -DE/DX = 0.0 !
! D60 D(12,3,4,6) -172.8141 -DE/DX = 0.0 !
! D61 D(13,3,4,5) 84.1997 -DE/DX = 0.0 !
! D62 D(13,3,4,6) -82.0635 -DE/DX = 0.0 !
! D63 D(14,3,4,5) 112.8115 -DE/DX = 0.0 !
! D64 D(14,3,4,6) -53.4517 -DE/DX = 0.0 !
! D65 D(2,4,6,1) 0.0 -DE/DX = 0.0 !
! D66 D(2,4,6,7) -40.4359 -DE/DX = 0.0 !
! D67 D(2,4,6,8) 125.9267 -DE/DX = 0.0 !
! D68 D(3,4,6,1) 40.436 -DE/DX = 0.0 !
! D69 D(3,4,6,7) 0.0 -DE/DX = 0.0 !
! D70 D(3,4,6,8) 166.3627 -DE/DX = 0.0 !
! D71 D(5,4,6,1) -125.9267 -DE/DX = 0.0 !
! D72 D(5,4,6,7) -166.3626 -DE/DX = 0.0 !
! D73 D(5,4,6,8) 0.0001 -DE/DX = 0.0 !
! D74 D(4,6,7,9) 172.8141 -DE/DX = 0.0 !
! D75 D(4,6,7,10) -33.1446 -DE/DX = 0.0 !
! D76 D(4,6,7,15) 82.0633 -DE/DX = 0.0 !
! D77 D(4,6,7,16) 53.4515 -DE/DX = 0.0 !
! D78 D(8,6,7,9) 6.5509 -DE/DX = 0.0 !
! D79 D(8,6,7,10) 160.5921 -DE/DX = 0.0 !
! D80 D(8,6,7,15) -84.2 -DE/DX = 0.0 !
! D81 D(8,6,7,16) -112.8118 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:DA TS OPT BERNY AM1 631gd pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:DA TS OPT BERNY AM1 631gd vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 524.81 cm-1. The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:DA TS OPT BERNY AM1 631gd vibration.gif]]

'''7. Thermochemistry'''
Sum of electronic and zero-point Energies= -234.403325
Sum of electronic and thermal Energies= -234.396907
Sum of electronic and thermal Enthalpies= -234.395963
Sum of electronic and thermal Free Energies= -234.432892

'''8. HOMO/LUMO visialisation'''
 
[[File:DA TS OPT BERNY AM1 631gd HOMOLUMO.png]]

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -234.54389655 a.u. || Cs
|}

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T15:24:03Z

Mh2710: /* Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

The table below showes the energies of reactants and transition states for 2 different calculation methods:3-21G and 6-31G(d).

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated using Ea= ETS-Er at 0 K and 298.15 K. These values are then compared to experimentally determined activation energies given in lab script.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

The activation energies calculated for both the chair and boat conformations using 6-31G(d) method have higher accuracy as they are less different compared to the experimental values. From the table we can see chair conformation has lower activation energy and so the reaction proceeds through this conformation. Bond formation is concerted from animation of the imaginary frequency. Dotted lines are shown for 6 bonds indicating aromatic character.

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11929 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== (c) Reoptimisation of transition state using B3LYP/6-31G(d) =====
'''1. Optimising transition state using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DA TS OPT BERNY AM1 631GD.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:DA TS OPT BERNY AM1 631GD.LOG| here]].

'''3. General information'''
 
[[File:DA TS OPT BERNY AM1 631gd info.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000496 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
Predicted change in Energy=-7.705534D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.386 -DE/DX = 0.0 !
! R2 R(1,6) 2.9004 -DE/DX = 0.0 !
! R3 R(1,7) 2.2725 -DE/DX = 0.0 !
! R4 R(1,9) 2.7536 -DE/DX = 0.0 !
! R5 R(1,10) 2.4251 -DE/DX = 0.0 !
! R6 R(1,15) 1.0842 -DE/DX = 0.0 !
! R7 R(1,16) 1.0863 -DE/DX = 0.0 !
! R8 R(2,3) 2.2725 -DE/DX = 0.0 !
! R9 R(2,4) 2.9004 -DE/DX = 0.0 !
! R10 R(2,11) 2.4251 -DE/DX = 0.0 !
! R11 R(2,12) 2.7536 -DE/DX = 0.0 !
! R12 R(2,13) 1.0842 -DE/DX = 0.0 !
! R13 R(2,14) 1.0863 -DE/DX = 0.0 !
! R14 R(3,4) 1.383 -DE/DX = 0.0 !
! R15 R(3,11) 1.084 -DE/DX = 0.0 !
! R16 R(3,12) 1.0873 -DE/DX = 0.0 !
! R17 R(3,13) 2.5399 -DE/DX = 0.0 !
! R18 R(3,14) 2.5323 -DE/DX = 0.0 !
! R19 R(4,5) 1.0891 -DE/DX = 0.0 !
! R20 R(4,6) 1.4072 -DE/DX = 0.0 !
! R21 R(6,7) 1.383 -DE/DX = 0.0 !
! R22 R(6,8) 1.0891 -DE/DX = 0.0 !
! R23 R(7,9) 1.0873 -DE/DX = 0.0 !
! R24 R(7,10) 1.084 -DE/DX = 0.0 !
! R25 R(7,15) 2.5399 -DE/DX = 0.0 !
! R26 R(7,16) 2.5323 -DE/DX = 0.0 !
! A1 A(2,1,6) 90.2098 -DE/DX = 0.0 !
! A2 A(2,1,7) 109.1164 -DE/DX = 0.0 !
! A3 A(2,1,9) 131.4998 -DE/DX = 0.0 !
! A4 A(2,1,10) 98.9089 -DE/DX = 0.0 !
! A5 A(2,1,15) 120.0522 -DE/DX = 0.0 !
! A6 A(2,1,16) 119.9852 -DE/DX = 0.0 !
! A7 A(6,1,9) 44.4899 -DE/DX = 0.0 !
! A8 A(6,1,10) 46.5393 -DE/DX = 0.0 !
! A9 A(6,1,15) 83.3596 -DE/DX = 0.0 !
! A10 A(6,1,16) 118.2474 -DE/DX = 0.0 !
! A11 A(9,1,10) 40.6754 -DE/DX = 0.0 !
! A12 A(9,1,15) 77.8409 -DE/DX = 0.0 !
! A13 A(9,1,16) 80.5628 -DE/DX = 0.0 !
! A14 A(10,1,15) 116.9474 -DE/DX = 0.0 !
! A15 A(10,1,16) 74.6439 -DE/DX = 0.0 !
! A16 A(15,1,16) 115.1638 -DE/DX = 0.0 !
! A17 A(1,2,3) 109.1165 -DE/DX = 0.0 !
! A18 A(1,2,4) 90.2099 -DE/DX = 0.0 !
! A19 A(1,2,11) 98.9089 -DE/DX = 0.0 !
! A20 A(1,2,12) 131.5 -DE/DX = 0.0 !
! A21 A(1,2,13) 120.0522 -DE/DX = 0.0 !
! A22 A(1,2,14) 119.9852 -DE/DX = 0.0 !
! A23 A(4,2,11) 46.5393 -DE/DX = 0.0 !
! A24 A(4,2,12) 44.49 -DE/DX = 0.0 !
! A25 A(4,2,13) 83.3596 -DE/DX = 0.0 !
! A26 A(4,2,14) 118.2474 -DE/DX = 0.0 !
! A27 A(11,2,12) 40.6755 -DE/DX = 0.0 !
! A28 A(11,2,13) 116.9475 -DE/DX = 0.0 !
! A29 A(11,2,14) 74.644 -DE/DX = 0.0 !
! A30 A(12,2,13) 77.8409 -DE/DX = 0.0 !
! A31 A(12,2,14) 80.5627 -DE/DX = 0.0 !
! A32 A(13,2,14) 115.1638 -DE/DX = 0.0 !
! A33 A(4,3,11) 120.6613 -DE/DX = 0.0 !
! A34 A(4,3,12) 120.0232 -DE/DX = 0.0 !
! A35 A(4,3,13) 94.0558 -DE/DX = 0.0 !
! A36 A(4,3,14) 127.3507 -DE/DX = 0.0 !
! A37 A(11,3,12) 114.4864 -DE/DX = 0.0 !
! A38 A(11,3,13) 109.2312 -DE/DX = 0.0 !
! A39 A(11,3,14) 69.5135 -DE/DX = 0.0 !
! A40 A(12,3,13) 88.6205 -DE/DX = 0.0 !
! A41 A(12,3,14) 91.9441 -DE/DX = 0.0 !
! A42 A(13,3,14) 42.3516 -DE/DX = 0.0 !
! A43 A(2,4,5) 121.3465 -DE/DX = 0.0 !
! A44 A(2,4,6) 89.7903 -DE/DX = 0.0 !
! A45 A(3,4,5) 118.6679 -DE/DX = 0.0 !
! A46 A(3,4,6) 122.0341 -DE/DX = 0.0 !
! A47 A(5,4,6) 117.9096 -DE/DX = 0.0 !
! A48 A(1,6,4) 89.7901 -DE/DX = 0.0 !
! A49 A(1,6,8) 121.3467 -DE/DX = 0.0 !
! A50 A(4,6,7) 122.0341 -DE/DX = 0.0 !
! A51 A(4,6,8) 117.9096 -DE/DX = 0.0 !
! A52 A(7,6,8) 118.6679 -DE/DX = 0.0 !
! A53 A(6,7,9) 120.0232 -DE/DX = 0.0 !
! A54 A(6,7,10) 120.6613 -DE/DX = 0.0 !
! A55 A(6,7,15) 94.0558 -DE/DX = 0.0 !
! A56 A(6,7,16) 127.3506 -DE/DX = 0.0 !
! A57 A(9,7,10) 114.4864 -DE/DX = 0.0 !
! A58 A(9,7,15) 88.6207 -DE/DX = 0.0 !
! A59 A(9,7,16) 91.9443 -DE/DX = 0.0 !
! A60 A(10,7,15) 109.2309 -DE/DX = 0.0 !
! A61 A(10,7,16) 69.5133 -DE/DX = 0.0 !
! A62 A(15,7,16) 42.3515 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -20.742 -DE/DX = 0.0 !
! D2 D(6,1,2,4) 0.0 -DE/DX = 0.0 !
! D3 D(6,1,2,11) -45.918 -DE/DX = 0.0 !
! D4 D(6,1,2,12) -18.3309 -DE/DX = 0.0 !
! D5 D(6,1,2,13) 82.445 -DE/DX = 0.0 !
! D6 D(6,1,2,14) -123.2664 -DE/DX = 0.0 !
! D7 D(7,1,2,3) -0.0001 -DE/DX = 0.0 !
! D8 D(7,1,2,4) 20.742 -DE/DX = 0.0 !
! D9 D(7,1,2,11) -25.1761 -DE/DX = 0.0 !
! D10 D(7,1,2,12) 2.4111 -DE/DX = 0.0 !
! D11 D(7,1,2,13) 103.1869 -DE/DX = 0.0 !
! D12 D(7,1,2,14) -102.5244 -DE/DX = 0.0 !
! D13 D(9,1,2,3) -2.4112 -DE/DX = 0.0 !
! D14 D(9,1,2,4) 18.3308 -DE/DX = 0.0 !
! D15 D(9,1,2,11) -27.5872 -DE/DX = 0.0 !
! D16 D(9,1,2,12) -0.0001 -DE/DX = 0.0 !
! D17 D(9,1,2,13) 100.7758 -DE/DX = 0.0 !
! D18 D(9,1,2,14) -104.9356 -DE/DX = 0.0 !
! D19 D(10,1,2,3) 25.176 -DE/DX = 0.0 !
! D20 D(10,1,2,4) 45.918 -DE/DX = 0.0 !
! D21 D(10,1,2,11) -0.0001 -DE/DX = 0.0 !
! D22 D(10,1,2,12) 27.5871 -DE/DX = 0.0 !
! D23 D(10,1,2,13) 128.3629 -DE/DX = 0.0 !
! D24 D(10,1,2,14) -77.3484 -DE/DX = 0.0 !
! D25 D(15,1,2,3) -103.1869 -DE/DX = 0.0 !
! D26 D(15,1,2,4) -82.4449 -DE/DX = 0.0 !
! D27 D(15,1,2,11) -128.3629 -DE/DX = 0.0 !
! D28 D(15,1,2,12) -100.7758 -DE/DX = 0.0 !
! D29 D(15,1,2,13) 0.0 -DE/DX = 0.0 !
! D30 D(15,1,2,14) 154.2887 -DE/DX = 0.0 !
! D31 D(16,1,2,3) 102.5243 -DE/DX = 0.0 !
! D32 D(16,1,2,4) 123.2663 -DE/DX = 0.0 !
! D33 D(16,1,2,11) 77.3483 -DE/DX = 0.0 !
! D34 D(16,1,2,12) 104.9354 -DE/DX = 0.0 !
! D35 D(16,1,2,13) -154.2888 -DE/DX = 0.0 !
! D36 D(16,1,2,14) -0.0001 -DE/DX = 0.0 !
! D37 D(2,1,6,4) 0.0 -DE/DX = 0.0 !
! D38 D(2,1,6,8) -123.0828 -DE/DX = 0.0 !
! D39 D(9,1,6,4) -160.3592 -DE/DX = 0.0 !
! D40 D(9,1,6,8) 76.5581 -DE/DX = 0.0 !
! D41 D(10,1,6,4) -102.1158 -DE/DX = 0.0 !
! D42 D(10,1,6,8) 134.8014 -DE/DX = 0.0 !
! D43 D(15,1,6,4) 120.2482 -DE/DX = 0.0 !
! D44 D(15,1,6,8) -2.8345 -DE/DX = 0.0 !
! D45 D(16,1,6,4) -124.7021 -DE/DX = 0.0 !
! D46 D(16,1,6,8) 112.2151 -DE/DX = 0.0 !
! D47 D(1,2,4,5) 123.0828 -DE/DX = 0.0 !
! D48 D(1,2,4,6) 0.0 -DE/DX = 0.0 !
! D49 D(11,2,4,5) -134.8015 -DE/DX = 0.0 !
! D50 D(11,2,4,6) 102.1157 -DE/DX = 0.0 !
! D51 D(12,2,4,5) -76.5581 -DE/DX = 0.0 !
! D52 D(12,2,4,6) 160.3591 -DE/DX = 0.0 !
! D53 D(13,2,4,5) 2.8345 -DE/DX = 0.0 !
! D54 D(13,2,4,6) -120.2482 -DE/DX = 0.0 !
! D55 D(14,2,4,5) -112.2151 -DE/DX = 0.0 !
! D56 D(14,2,4,6) 124.7022 -DE/DX = 0.0 !
! D57 D(11,3,4,5) -160.592 -DE/DX = 0.0 !
! D58 D(11,3,4,6) 33.1448 -DE/DX = 0.0 !
! D59 D(12,3,4,5) -6.5509 -DE/DX = 0.0 !
! D60 D(12,3,4,6) -172.8141 -DE/DX = 0.0 !
! D61 D(13,3,4,5) 84.1997 -DE/DX = 0.0 !
! D62 D(13,3,4,6) -82.0635 -DE/DX = 0.0 !
! D63 D(14,3,4,5) 112.8115 -DE/DX = 0.0 !
! D64 D(14,3,4,6) -53.4517 -DE/DX = 0.0 !
! D65 D(2,4,6,1) 0.0 -DE/DX = 0.0 !
! D66 D(2,4,6,7) -40.4359 -DE/DX = 0.0 !
! D67 D(2,4,6,8) 125.9267 -DE/DX = 0.0 !
! D68 D(3,4,6,1) 40.436 -DE/DX = 0.0 !
! D69 D(3,4,6,7) 0.0 -DE/DX = 0.0 !
! D70 D(3,4,6,8) 166.3627 -DE/DX = 0.0 !
! D71 D(5,4,6,1) -125.9267 -DE/DX = 0.0 !
! D72 D(5,4,6,7) -166.3626 -DE/DX = 0.0 !
! D73 D(5,4,6,8) 0.0001 -DE/DX = 0.0 !
! D74 D(4,6,7,9) 172.8141 -DE/DX = 0.0 !
! D75 D(4,6,7,10) -33.1446 -DE/DX = 0.0 !
! D76 D(4,6,7,15) 82.0633 -DE/DX = 0.0 !
! D77 D(4,6,7,16) 53.4515 -DE/DX = 0.0 !
! D78 D(8,6,7,9) 6.5509 -DE/DX = 0.0 !
! D79 D(8,6,7,10) 160.5921 -DE/DX = 0.0 !
! D80 D(8,6,7,15) -84.2 -DE/DX = 0.0 !
! D81 D(8,6,7,16) -112.8118 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:DA TS OPT BERNY AM1 631gd pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:DA TS OPT BERNY AM1 631gd vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 524.81 cm-1. The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:DA TS OPT BERNY AM1 631gd vibration.gif]]

'''7. Thermochemistry'''
Sum of electronic and zero-point Energies= -234.403325
Sum of electronic and thermal Energies= -234.396907
Sum of electronic and thermal Enthalpies= -234.395963
Sum of electronic and thermal Free Energies= -234.432892

'''8. HOMO/LUMO visialisation'''
 
[[File:DA TS OPT BERNY AM1 631gd HOMOLUMO.png]]

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -234.54389655 a.u. || Cs
|}

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T14:49:00Z

Mh2710: /* Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

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

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

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

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.20
| align="center" | 44.7 ± 2.0
|}

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

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11929 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== (c) Reoptimisation of transition state using B3LYP/6-31G(d) =====
'''1. Optimising transition state using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DA TS OPT BERNY AM1 631GD.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:DA TS OPT BERNY AM1 631GD.LOG| here]].

'''3. General information'''
 
[[File:DA TS OPT BERNY AM1 631gd info.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000496 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
Predicted change in Energy=-7.705534D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.386 -DE/DX = 0.0 !
! R2 R(1,6) 2.9004 -DE/DX = 0.0 !
! R3 R(1,7) 2.2725 -DE/DX = 0.0 !
! R4 R(1,9) 2.7536 -DE/DX = 0.0 !
! R5 R(1,10) 2.4251 -DE/DX = 0.0 !
! R6 R(1,15) 1.0842 -DE/DX = 0.0 !
! R7 R(1,16) 1.0863 -DE/DX = 0.0 !
! R8 R(2,3) 2.2725 -DE/DX = 0.0 !
! R9 R(2,4) 2.9004 -DE/DX = 0.0 !
! R10 R(2,11) 2.4251 -DE/DX = 0.0 !
! R11 R(2,12) 2.7536 -DE/DX = 0.0 !
! R12 R(2,13) 1.0842 -DE/DX = 0.0 !
! R13 R(2,14) 1.0863 -DE/DX = 0.0 !
! R14 R(3,4) 1.383 -DE/DX = 0.0 !
! R15 R(3,11) 1.084 -DE/DX = 0.0 !
! R16 R(3,12) 1.0873 -DE/DX = 0.0 !
! R17 R(3,13) 2.5399 -DE/DX = 0.0 !
! R18 R(3,14) 2.5323 -DE/DX = 0.0 !
! R19 R(4,5) 1.0891 -DE/DX = 0.0 !
! R20 R(4,6) 1.4072 -DE/DX = 0.0 !
! R21 R(6,7) 1.383 -DE/DX = 0.0 !
! R22 R(6,8) 1.0891 -DE/DX = 0.0 !
! R23 R(7,9) 1.0873 -DE/DX = 0.0 !
! R24 R(7,10) 1.084 -DE/DX = 0.0 !
! R25 R(7,15) 2.5399 -DE/DX = 0.0 !
! R26 R(7,16) 2.5323 -DE/DX = 0.0 !
! A1 A(2,1,6) 90.2098 -DE/DX = 0.0 !
! A2 A(2,1,7) 109.1164 -DE/DX = 0.0 !
! A3 A(2,1,9) 131.4998 -DE/DX = 0.0 !
! A4 A(2,1,10) 98.9089 -DE/DX = 0.0 !
! A5 A(2,1,15) 120.0522 -DE/DX = 0.0 !
! A6 A(2,1,16) 119.9852 -DE/DX = 0.0 !
! A7 A(6,1,9) 44.4899 -DE/DX = 0.0 !
! A8 A(6,1,10) 46.5393 -DE/DX = 0.0 !
! A9 A(6,1,15) 83.3596 -DE/DX = 0.0 !
! A10 A(6,1,16) 118.2474 -DE/DX = 0.0 !
! A11 A(9,1,10) 40.6754 -DE/DX = 0.0 !
! A12 A(9,1,15) 77.8409 -DE/DX = 0.0 !
! A13 A(9,1,16) 80.5628 -DE/DX = 0.0 !
! A14 A(10,1,15) 116.9474 -DE/DX = 0.0 !
! A15 A(10,1,16) 74.6439 -DE/DX = 0.0 !
! A16 A(15,1,16) 115.1638 -DE/DX = 0.0 !
! A17 A(1,2,3) 109.1165 -DE/DX = 0.0 !
! A18 A(1,2,4) 90.2099 -DE/DX = 0.0 !
! A19 A(1,2,11) 98.9089 -DE/DX = 0.0 !
! A20 A(1,2,12) 131.5 -DE/DX = 0.0 !
! A21 A(1,2,13) 120.0522 -DE/DX = 0.0 !
! A22 A(1,2,14) 119.9852 -DE/DX = 0.0 !
! A23 A(4,2,11) 46.5393 -DE/DX = 0.0 !
! A24 A(4,2,12) 44.49 -DE/DX = 0.0 !
! A25 A(4,2,13) 83.3596 -DE/DX = 0.0 !
! A26 A(4,2,14) 118.2474 -DE/DX = 0.0 !
! A27 A(11,2,12) 40.6755 -DE/DX = 0.0 !
! A28 A(11,2,13) 116.9475 -DE/DX = 0.0 !
! A29 A(11,2,14) 74.644 -DE/DX = 0.0 !
! A30 A(12,2,13) 77.8409 -DE/DX = 0.0 !
! A31 A(12,2,14) 80.5627 -DE/DX = 0.0 !
! A32 A(13,2,14) 115.1638 -DE/DX = 0.0 !
! A33 A(4,3,11) 120.6613 -DE/DX = 0.0 !
! A34 A(4,3,12) 120.0232 -DE/DX = 0.0 !
! A35 A(4,3,13) 94.0558 -DE/DX = 0.0 !
! A36 A(4,3,14) 127.3507 -DE/DX = 0.0 !
! A37 A(11,3,12) 114.4864 -DE/DX = 0.0 !
! A38 A(11,3,13) 109.2312 -DE/DX = 0.0 !
! A39 A(11,3,14) 69.5135 -DE/DX = 0.0 !
! A40 A(12,3,13) 88.6205 -DE/DX = 0.0 !
! A41 A(12,3,14) 91.9441 -DE/DX = 0.0 !
! A42 A(13,3,14) 42.3516 -DE/DX = 0.0 !
! A43 A(2,4,5) 121.3465 -DE/DX = 0.0 !
! A44 A(2,4,6) 89.7903 -DE/DX = 0.0 !
! A45 A(3,4,5) 118.6679 -DE/DX = 0.0 !
! A46 A(3,4,6) 122.0341 -DE/DX = 0.0 !
! A47 A(5,4,6) 117.9096 -DE/DX = 0.0 !
! A48 A(1,6,4) 89.7901 -DE/DX = 0.0 !
! A49 A(1,6,8) 121.3467 -DE/DX = 0.0 !
! A50 A(4,6,7) 122.0341 -DE/DX = 0.0 !
! A51 A(4,6,8) 117.9096 -DE/DX = 0.0 !
! A52 A(7,6,8) 118.6679 -DE/DX = 0.0 !
! A53 A(6,7,9) 120.0232 -DE/DX = 0.0 !
! A54 A(6,7,10) 120.6613 -DE/DX = 0.0 !
! A55 A(6,7,15) 94.0558 -DE/DX = 0.0 !
! A56 A(6,7,16) 127.3506 -DE/DX = 0.0 !
! A57 A(9,7,10) 114.4864 -DE/DX = 0.0 !
! A58 A(9,7,15) 88.6207 -DE/DX = 0.0 !
! A59 A(9,7,16) 91.9443 -DE/DX = 0.0 !
! A60 A(10,7,15) 109.2309 -DE/DX = 0.0 !
! A61 A(10,7,16) 69.5133 -DE/DX = 0.0 !
! A62 A(15,7,16) 42.3515 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -20.742 -DE/DX = 0.0 !
! D2 D(6,1,2,4) 0.0 -DE/DX = 0.0 !
! D3 D(6,1,2,11) -45.918 -DE/DX = 0.0 !
! D4 D(6,1,2,12) -18.3309 -DE/DX = 0.0 !
! D5 D(6,1,2,13) 82.445 -DE/DX = 0.0 !
! D6 D(6,1,2,14) -123.2664 -DE/DX = 0.0 !
! D7 D(7,1,2,3) -0.0001 -DE/DX = 0.0 !
! D8 D(7,1,2,4) 20.742 -DE/DX = 0.0 !
! D9 D(7,1,2,11) -25.1761 -DE/DX = 0.0 !
! D10 D(7,1,2,12) 2.4111 -DE/DX = 0.0 !
! D11 D(7,1,2,13) 103.1869 -DE/DX = 0.0 !
! D12 D(7,1,2,14) -102.5244 -DE/DX = 0.0 !
! D13 D(9,1,2,3) -2.4112 -DE/DX = 0.0 !
! D14 D(9,1,2,4) 18.3308 -DE/DX = 0.0 !
! D15 D(9,1,2,11) -27.5872 -DE/DX = 0.0 !
! D16 D(9,1,2,12) -0.0001 -DE/DX = 0.0 !
! D17 D(9,1,2,13) 100.7758 -DE/DX = 0.0 !
! D18 D(9,1,2,14) -104.9356 -DE/DX = 0.0 !
! D19 D(10,1,2,3) 25.176 -DE/DX = 0.0 !
! D20 D(10,1,2,4) 45.918 -DE/DX = 0.0 !
! D21 D(10,1,2,11) -0.0001 -DE/DX = 0.0 !
! D22 D(10,1,2,12) 27.5871 -DE/DX = 0.0 !
! D23 D(10,1,2,13) 128.3629 -DE/DX = 0.0 !
! D24 D(10,1,2,14) -77.3484 -DE/DX = 0.0 !
! D25 D(15,1,2,3) -103.1869 -DE/DX = 0.0 !
! D26 D(15,1,2,4) -82.4449 -DE/DX = 0.0 !
! D27 D(15,1,2,11) -128.3629 -DE/DX = 0.0 !
! D28 D(15,1,2,12) -100.7758 -DE/DX = 0.0 !
! D29 D(15,1,2,13) 0.0 -DE/DX = 0.0 !
! D30 D(15,1,2,14) 154.2887 -DE/DX = 0.0 !
! D31 D(16,1,2,3) 102.5243 -DE/DX = 0.0 !
! D32 D(16,1,2,4) 123.2663 -DE/DX = 0.0 !
! D33 D(16,1,2,11) 77.3483 -DE/DX = 0.0 !
! D34 D(16,1,2,12) 104.9354 -DE/DX = 0.0 !
! D35 D(16,1,2,13) -154.2888 -DE/DX = 0.0 !
! D36 D(16,1,2,14) -0.0001 -DE/DX = 0.0 !
! D37 D(2,1,6,4) 0.0 -DE/DX = 0.0 !
! D38 D(2,1,6,8) -123.0828 -DE/DX = 0.0 !
! D39 D(9,1,6,4) -160.3592 -DE/DX = 0.0 !
! D40 D(9,1,6,8) 76.5581 -DE/DX = 0.0 !
! D41 D(10,1,6,4) -102.1158 -DE/DX = 0.0 !
! D42 D(10,1,6,8) 134.8014 -DE/DX = 0.0 !
! D43 D(15,1,6,4) 120.2482 -DE/DX = 0.0 !
! D44 D(15,1,6,8) -2.8345 -DE/DX = 0.0 !
! D45 D(16,1,6,4) -124.7021 -DE/DX = 0.0 !
! D46 D(16,1,6,8) 112.2151 -DE/DX = 0.0 !
! D47 D(1,2,4,5) 123.0828 -DE/DX = 0.0 !
! D48 D(1,2,4,6) 0.0 -DE/DX = 0.0 !
! D49 D(11,2,4,5) -134.8015 -DE/DX = 0.0 !
! D50 D(11,2,4,6) 102.1157 -DE/DX = 0.0 !
! D51 D(12,2,4,5) -76.5581 -DE/DX = 0.0 !
! D52 D(12,2,4,6) 160.3591 -DE/DX = 0.0 !
! D53 D(13,2,4,5) 2.8345 -DE/DX = 0.0 !
! D54 D(13,2,4,6) -120.2482 -DE/DX = 0.0 !
! D55 D(14,2,4,5) -112.2151 -DE/DX = 0.0 !
! D56 D(14,2,4,6) 124.7022 -DE/DX = 0.0 !
! D57 D(11,3,4,5) -160.592 -DE/DX = 0.0 !
! D58 D(11,3,4,6) 33.1448 -DE/DX = 0.0 !
! D59 D(12,3,4,5) -6.5509 -DE/DX = 0.0 !
! D60 D(12,3,4,6) -172.8141 -DE/DX = 0.0 !
! D61 D(13,3,4,5) 84.1997 -DE/DX = 0.0 !
! D62 D(13,3,4,6) -82.0635 -DE/DX = 0.0 !
! D63 D(14,3,4,5) 112.8115 -DE/DX = 0.0 !
! D64 D(14,3,4,6) -53.4517 -DE/DX = 0.0 !
! D65 D(2,4,6,1) 0.0 -DE/DX = 0.0 !
! D66 D(2,4,6,7) -40.4359 -DE/DX = 0.0 !
! D67 D(2,4,6,8) 125.9267 -DE/DX = 0.0 !
! D68 D(3,4,6,1) 40.436 -DE/DX = 0.0 !
! D69 D(3,4,6,7) 0.0 -DE/DX = 0.0 !
! D70 D(3,4,6,8) 166.3627 -DE/DX = 0.0 !
! D71 D(5,4,6,1) -125.9267 -DE/DX = 0.0 !
! D72 D(5,4,6,7) -166.3626 -DE/DX = 0.0 !
! D73 D(5,4,6,8) 0.0001 -DE/DX = 0.0 !
! D74 D(4,6,7,9) 172.8141 -DE/DX = 0.0 !
! D75 D(4,6,7,10) -33.1446 -DE/DX = 0.0 !
! D76 D(4,6,7,15) 82.0633 -DE/DX = 0.0 !
! D77 D(4,6,7,16) 53.4515 -DE/DX = 0.0 !
! D78 D(8,6,7,9) 6.5509 -DE/DX = 0.0 !
! D79 D(8,6,7,10) 160.5921 -DE/DX = 0.0 !
! D80 D(8,6,7,15) -84.2 -DE/DX = 0.0 !
! D81 D(8,6,7,16) -112.8118 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:DA TS OPT BERNY AM1 631gd pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:DA TS OPT BERNY AM1 631gd vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 524.81 cm-1. The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:DA TS OPT BERNY AM1 631gd vibration.gif]]

'''7. Thermochemistry'''
Sum of electronic and zero-point Energies= -234.403325
Sum of electronic and thermal Energies= -234.396907
Sum of electronic and thermal Enthalpies= -234.395963
Sum of electronic and thermal Free Energies= -234.432892

'''8. HOMO/LUMO visialisation'''
 
[[File:DA TS OPT BERNY AM1 631gd HOMOLUMO.png]]

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -234.54389655 a.u. || Cs
|}

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}

Rep:Mod:mh2710tata2

2013-03-15T14:01:19Z

Mh2710: /* Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures */

= Computational Lab, Module 3 =

In this module, we characterised transition structures in larger molecules for the Cope Rearrangement and the Diels-Alder reaction.

Shapes of optimised starting materials, products and transition structures were calculated as well as reaction pathways and barrier heights.

= The Cope Rearrangement tutorial =

The Cope Rearrangement of 1,5-hexadiene was studied in this module. This [3,3]-sigmatropic rearrangement is an example of pericyclic reaction which has a cyclic-geometric transition state and its reaction progresses are in a concerted fashion.

[[File:mh-Cope-Rearrangement.PNG|thumb|centre|300px|Cope Rearrangement]]

To determine the mechanism of the Cope Rearrangement, different comformations (6 gauche and 4 anti) of 1,5-hexadiene were calculated and compared.

=== Optimising the Reactants and Products ===

==== (a) Optimisation of 1,5-hexadiene with an "anti" central linkage ====

A 1,5-hexadiene molecule was drawn by combing a ethyl fragment and two vinyl fragments together and its dihedral angles were modified to give an anti-central linkage. This 1,5-hexadiene molecule was then optimiesd with HF/3-21G.

'''1. Optimising 1,5-hexadiene (anti) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti-1.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti-1.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001357 0.001800 YES
RMS Displacement 0.000459 0.001200 YES
Predicted change in Energy=-2.090841D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-anti1-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69260235 a.u. || C2
|}

==== (b) Optimisation of 1,5-hexadiene with an "gauche" central linkage ====

This molecule was drawn by changing the dihedral angles of the molecule in (a).

'''1. Optimising 1,5-hexadiene (gauche) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-gauche-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-gauche-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-gauche-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-3.377162D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-gauche-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Linkage !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Gauche || Optimisation to a minimum || HF || 3-21G || 250 MB || -231.69266122 a.u. || C1
|}

'''7. Comparison with (a)'''
 
{| class="wikitable" border="1"
! Energy (a) !! Energy (b) !! Energy difference (b)-(a)
|-
| -231.69260235 a.u. || -231.69266122 a.u. || -0.00005887 a.u.
|}

Higher energy was expected than (a) as two vinyl groups are closer in space leading to larger steric repulsion. However, the final energy of the optimised gauche structure is lower and the energy difference is equal to 0.00005887 a.u.(or 0.0369414 kcal/mol).

This is because the gauche conformation has a better sigma-sigma* interaction between bonding C-C orbital and antiperiplanar antibonding C-H orbital compared to the anti conformation. Moreover, goauche3 conformation is the most stable because good C-H-pi interaction between two vinyl groups. The H on one vinyl group is delta+ due to its sp2 geometry, so it has good interaction with electron rich pi orbital on the other vinyl group.

==== (c) Optimisation of lowest energy conformation of 1,5-hexadiene ====

Results exactly as (b).

==== (d) Identification of optimised structures ====
{| class="wikitable" border="1"
! Optimised stucture !! Conformer identified from Appendix 1
|-
| (a) || Anti1
|-
| (b) || Gauche3
|-
| (c) || Gauche3
|}

==== (e) Optimisation of anti2 conformer using HF/3-21G ====
'''1. Optimising 1,5-hexadiene (anti2) using HF/3-21G'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000564 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-5.156886D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || HF || 3-21G || Default || -231.69253525 a.u. || Ci
|}

'''7. Comparison with Appendix 1'''
 
{| class="wikitable" border="1"
! Energy (optimised) !! Energy (Appendix 1)
|-
| -231.69253525 a.u. || -231.69254 a.u.
|}
The energy for the optimised structure is very similar to the energy of anti2 comformation in Appendix 1, confirming the structures are the same.

==== (f) Reoptimisation of anti2 conformer using B3LYP/6-31G(d) ====
In this section, I reoptimised the previously HF/3-21G optimised anti2 1,5-hexadiene using a better method and basis set i.e. B3LYP/6-31G(d) in order to obtain a more accurate energy minimum.

'''1. Optimising 1,5-hexadiene (anti2) using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-anti2-631-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-anti2-631-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000260 0.001800 YES
RMS Displacement 0.000089 0.001200 YES
Predicted change in Energy=-1.717103D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-anti2-631-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Anti2 || Optimisation to a minimum || B3LYP || 6-31G(d) || Default || -234.61171035 a.u. || Ci
|}

'''7. Comparison with (e)'''
 
{| class="wikitable" border="1"
! Energy (HF/3-21G) !! Energy (B3LYP/6-31G(d)) !! Energy difference
|-
| -231.69253525 a.u. || -234.61171035 a.u. || 2.91916830 a.u.
|}
The energy of B3LYP/6-31G(d) optimised structure is much lower than that of HF/3-21G optimised structure, and the energy difference is equal to 2.91916830 a.u.(or 1831.80575 kcal/mol). However, there are no visible differences between the two structures by simply looking at their structures on GaussView as the following is shown.
{| class="wikitable" border="1"
! !! HF/3-21G !! B3LYP/6-31G(d)
|-
! Structure || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-opti.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>mh-hexadiene-anti2-631-opti.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

To find the out the change in geometry responsible for the large energy difference, the geometric data between the two structures were compared and showed by the table below.
[[File:mh-hexadiene-anti2-number.png|500px|thumb|A GaussView image of an anti2 1,5-hexadiene molecule.]]
{| class="wikitable" border="1"
! Geometric parameter !! HF/3-21G !! B3LYP/6-31G(d)
|-
| C1=C2 (or C5=C6) bond length || 1.31615 Å || 1.33352 Å
|-
| C2-C3 (or C4-C5) bond length || 1.50880 Å || 1.50421 Å
|-
| C3-C4 bond length || 1.55284 Å || 1.54808 Å
|-
| C1=C2-C3-C4 (or C3-C4-C5=C6) dihedral angle || +(or-)114.68828o || +(or-)118.58831o
|}
From the data above, geometry change was very small and negligible. The largest difference was in dihedral angles and this may cause large energy difference as the double bonds have a better alignment with the neighbouring C-C/C-H bonds, resulting in strong σ-π conjugations and thus have a large stablisation in energy for the B3LYP/6-31G(d) optimised structure.

==== (g) Frequency analysis of optimised anti2 structure ====

The frequency analysis is the second derivative of the potential energy surface of a reaction. The previous optimisation was done properly only if all the vibrational frequencies are real and positive.

===== Frequency analysis of B3LYP/6-31G(d) optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-freq.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre> Low frequencies --- -9.4878 -0.0002 0.0005 0.0008 3.7496 13.0251
Low frequencies --- 74.2865 80.9989 121.4178</pre>

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-vibfreq.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised to a minimum.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || B3LYP || 6-31G(d) || Default || -234.61171035 a.u.
|}

===== Frequency analysis of HF/3-21G optimised anti2 structure =====
'''1. File link'''
 
The frequency analysed file is linked to [[Media:mh-hexadiene-anti2-321-freq.LOG| here]].

'''2. General information'''
 
[[File:mh-hexadiene-anti2-321-freq-sum.PNG]]

The energy is the same as that obtained in optimisation, which means the structure is correct (i.e. the same as the optimised structure).

'''3. Real output'''
<pre>Low frequencies --- -2.2094 -1.6189 -0.0006 -0.0003 -0.0001 6.2740
Low frequencies --- 71.3382 85.7693 116.2625</pre>

The low frequencies are within ±15 cm-1.

'''4. Vibrational frequencies'''
 
[[File:mh-hexadiene-anti2-321-freq-vib.PNG]]

All vibrational frequencies are real and positive, indicating the molecule is fully optimised.

'''5. IR spectrum'''
 
[[File:mh-hexadiene-anti2-321-freq-IR.PNG|700px]]

From the vibrational frequencie table and the IR spectrum above, many vibrations have 0 IR absorption intensity therefore are not shown on the spectrum. This is due to hexadiene anti2 conformation is under Ci symmetry hence it is very symmetric. Some symmetric stretches may cancel each other out and therefore IR inactive.

'''6. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.539540
Sum of electronic and thermal Energies= -231.532567
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570913</pre>

'''7. Key information'''
 
{| class="wikitable" border="1"
! Conformer !! Job type !! Method !! Basis set !! Memory limit !! Energy
|-
| Anti2 || Frequency || HF || 3-21G || Default || -231.69253525 a.u.
|}

=== Optimising the "Chair" and "Boat" Transition Structures ===

==== (a) Optimisation of allyl fragment ====
In order to build up the transition state, an optimised allyl fragment is needed, which can combine with another one in two different orientations to give the chair or boat structure.

'''1. Optimising allyl fragment using HF/3-21G'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! style="text-align: centre;"|[[File:mh-allyl-321-opti.PNG|thumb|500px]]
|}

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-321-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-321-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000157 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000636 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-7.608588D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-321-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Fragment !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Allyl || Optimisation to a minimum || HF || 3-21G || Default || -115.82304004 a.u. || C2v
|}

==== (b) Optimisation of chair transition state by computing force constants ====
This optimisation method is very easy and quick, but it only works well for any guess transition state that is already close enough to the exact structure.

'''1. Optimising chair transition state using Berny method with force constants calculation'''
 
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-allyl-chair-opt-freq.PNG|thumb|300px]]
! style="text-align: centre;"|[[File:Appendix2a.jpg|thumb|500px]]
|}

The optimised structure looks very similar to the one in Appendix 2 on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-opt-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-opt-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000600 0.001800 YES
RMS Displacement 0.000150 0.001200 YES
Predicted change in Energy=-2.948570D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-opt-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-opt-freq-vib-freq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 818.02 cm-1. The corresponding vibrational mode is shown below, in which two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. This is exactly what happens in the Cope rearrangement, that is, one C-C bond forms and one C-C bond breaks at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-allyl-chair-opt-freq.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495205</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || HF || 3-21G || Default || -231.61932245 a.u. || C2h
|}

==== (c) Optimisation of chair transition state using frozen coordinate method ====
(c)&(d) together is another way of optimisation which is more reliable and gives a better result, but more time-consuming.

'''1. Optimising chair transition state with frozen coordinates'''
 
[[File:mh-allyl-chair-fro-coordi-opti-re.PNG|300px|thumb|right|A GaussView image of an optimised chair transition state with frozen coordinate.]]
This optimised structure looks a lot like the one optimised in (b). However, as the GaussView image is shown on the right, the optimised structure has a fixed bond distance of 2.2 Å for the terminal C atoms of the allyl fragments.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-fro-coordi-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-sum-re.PNG]]

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000778 0.001800 YES
RMS Displacement 0.000204 0.001200 YES
Predicted change in Energy=-5.318408D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-fro-coordi-opti-pointgroup-re.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.61402467 a.u. || C2
|}

==== (d) Reoptimisation of chair transition state with unfrozen coordinates ====
'''1. Optimising chair transition state using Berny method without force constants calculation'''
 
[[File:mh-allyl-chair-non-froze.PNG|300px|thumb|right|A GaussView image of a optimised chair transition state using the redundant coordinate editor.]]
As the GaussView image is shown on the right, this optimised structure looks almost the same as the one optimised in (b).

'''2. File link'''
 
The optimised file is linked to [[Media:mh-allyl-chair-non-froze.LOG| here]].

'''3. General information'''
 
[[File:mh-allyl-chair-non-froze-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001666 0.001800 YES
RMS Displacement 0.000315 0.001200 YES
Predicted change in Energy=-3.021453D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-allyl-chair-non-froze-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-allyl-chair-non-froze-vibrationfreq.gif]]

Smilarly to (b), there is also only one imaginary frequency of about -818 cm-1. The corresponding vibrational mode is shown above, and the motion is similar to that of the structure obtained in (b).

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.466705
Sum of electronic and thermal Energies= -231.461344
Sum of electronic and thermal Enthalpies= -231.460400
Sum of electronic and thermal Free Energies= -231.495211</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny) || HF || 3-21G || Default || -231.61932157 a.u. || C2h
|}

'''9. Comparison to (b)'''
{| class="wikitable" border="1"
! Bond forming/breaking distances (b) !! Bond forming/breaking distances (d)
|-
| 2.02026 Å || 2.02057Å
|}
The bond forming/breaking distances of the optimised structure using the redundant coordinate editor are just slightly lower than that of the optimised structure by computing the force constants.

==== (e) Optimisation of boat transition state using QST2 method ====
===== First optimisation from optimised anti2 1,5-hexadiene =====
'''1. Optimising boat transition state from optimised anti2 1,5-hexadiene'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant1.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product1.PNG|thumb|250px|product]]
|}

The QST2 method does not give the correct boat structure using these reactant and product structures shown above. The optimisation failed and we obtained the structure shown below which looks a bit like the chair transition state but more dissociated.

===== Second optimisation from modified reactant and product =====
'''1. Optimising boat transition state from modified reactant and product'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-reactant2.PNG|thumb|250px|reactant]]
! style="text-align: centre;"|[[Image:mh-hexadiene-boat-product2.PNG|thumb|250px|product]]
|}

As the above GaussView image is shown, the reactant and product structures are modified to become closer to the boat transition state so that it is easier to obtain the correct boat structure.

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:mh-hexadiene-boat-opti-freq.PNG|thumb|250px|optimised transition state]]
! style="text-align: centre;"|[[Image:Appendix2b.jpg|thumb|400px|C2v boat transition state shown in Appendix 2.]]
|}

The optimised structure shown above is boat-like and is very similar to the one in Appendix 2 shown on the right.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-hexadiene-boat-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-hexadiene-boat-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-5.651889D-08
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-hexadiene-boat-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-hexadiene-boat-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 839.62 cm-1. The corresponding vibrational mode is shown below. Although the geometry is different, the boat structure has a similar vibrational motion as the chair structure obtained earlier, that is, two nearby terminal C atoms of the two allyl fragments approach each other in a sychronised motion and facilitates a bond formation, while the other pair of terminal C atoms move away from each other in a sychronised motion and represents a bond breaking. Again, the bond forming and breaking happens at the same time.

[[File:mh-hexadiene-boat-transition2.gif|thumb|centre|300px|animation of boat transition state]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= -231.450924
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444351
Sum of electronic and thermal Free Energies= -231.479769</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (QST2)+freq || HF || 3-21G || Default || -231.60280243 a.u. || C2v
|}

==== (f) IRC analysis of optimised chair and boat transition states ====
===== IRC analysis of optimised chair transition state =====

'''1. Calculating minimum energy path from chair transition state'''
 
[[File:mh-chair-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 44 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-chair-IRC-re.LOG| here]].

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-chair-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:mh-chair-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-chair-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-chair-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Chair || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.69157889 a.u. || C2
|}

'''6. IRC plot of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-CHAIR-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-CHAIR-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the energy minimum is not reached in this calculation because the RMS gradient does not reach 0 in the end. Now there are three options can be used to give a more accurate and reliable result: (1) run normal minimisation on the last point of this IRC calculation, (2) redo the IRC calculation to compute a larger number of points until the minimum is reached, (3) redo the IRC calculation to compute the force constants at every step. As the RMS gradient is very close to 0 already, I decided to try the first approach in the following.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.408598D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a minimum || HF || 3-21G || Default || -231.69166702 a.u. || C2
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-chair-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch2 conformation that connect chair transition state to the boat as it's the last point of IRC pathway.

===== IRC analysis of optimised boat transition state =====
'''1. Calculating minimum energy path from boat transition state'''
 
[[File:mh-boat-IRC.gif|centre]]

As the reaction coordinate is symmetrical in the cope rearrangement, "forward only" is chosen for this IRC calculation. There are 45 intermediate geometries obtianed, which are connected together to show the geometric change following the calculated minimum energy path from the boat transition structure to either reactant or product.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-boat-IRC.LOG| here]]

'''3. General information of the first&last point of the IRC calculation'''
{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-first.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[Image:mh-boat-irc-first-sum.PNG|thumb|250px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 45) '''
! scope="row" style="text-align: left;"| [[File:mh-boat-irc-last.PNG|thumb|250px|Structure]]
! style="text-align: centre;"|[[File:mh-boat-irc-last-sum.PNG|thumb|250px|Summary]]
|}

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Symmetry information of the last point of the IRC calculation'''
 
[[File:Mh-boat-irc-last-sum-pointgroup.PNG]]

'''5. Key information of the IRC calculation'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy of the last point !! Point group of the last point
|-
| Boat || IRC, forward only, calculate always, compute 50 points || HF || 3-21G || Default || -231.68298213 a.u. || Cs
|}

'''6. IRC plot of the IRC calculation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-IRC-boat-ENERGY.PNG|thumb|300px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:mh-IRC-boat-GRADIENT.PNG|thumb|300px|(2) RMS Gradient Norm along IRC]]
|}

As the IRC plot is shown above, the RMS gradient is very close to 0 but not exactly equal to 0, so I decided to run a normal minimisation for the last point of this IRC calculation in order to obtain a more accurate minimum.

===== Further optimisation =====
'''1. Optimising the last point of the IRC calculation using HF/3-21G'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure looks almost the same as the one before optimisation.

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-IRC-last-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-IRC-last-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete. And the energy is the minimum I found, which is only slightly lower than that before optimisation.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000402 0.001800 YES
RMS Displacement 0.000112 0.001200 YES
Predicted change in Energy=-3.711368D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-IRC-last-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| boat || Optimisation to a minimum || HF || 3-21G || Default || -231.68302550 a.u. || Cs
|}

===== Questions =====

'''Which conformers of 1,5-hexadiene do you think they connect?'''

[[File:mh-boat-IRC-last-opti.PNG|thumb|centre|250px|Optimised structure]]

The structure above is the gauch5 conformation that connect boat transition state to the chair as it's the last point of IRC pathway.

==== (g) Reoptimisation of chair and boat transition states using B3LYP/6-31G(d) ====
===== Reoptimisation of chair transition state =====
'''1. Optimising chair transition state using B3LYP/6-31G(d)'''

[[File:mh-chair-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-chair-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-chair-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000108 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.281366D-09
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-chair-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2h, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-chair-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-chair-631-opti-freq-vibration.gif]]

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

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Chair || Optimisation to a TS (Berny), calculate the force constants once || B3LYP || 6-31G(d) || Default || -234.55698303 a.u. || C2h
|}

===== Reoptimisation of boat transition state =====

'''1. Optimising boat transition state using B3LYP/6-31G(d)'''

[[File:mh-boat-631-opti-freq.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-boat-631-opti-freq.LOG| here]].

'''3. General information'''
 
[[File:mh-boat-631-opti-freq-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000695 0.001800 YES
RMS Displacement 0.000159 0.001200 YES
Predicted change in Energy=-3.028451D-08
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-boat-631-opti-freq-pointgroup.PNG]]

The point group of the optimised structure is C2v, confirming the structure is correct.

'''6. Vibrational frequencies'''
 
[[File:mh-boat-631-opti-freq-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 565.53 cm-1 which is lower than that of the HF/3-21G optimised structure (i.e. 818.02 cm-1). The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:mh-boat-631-opti-freq-vibration.gif]]

'''7. Thermochemistry'''
<pre>Sum of electronic and zero-point Energies= -234.402339
Sum of electronic and thermal Energies= -234.396006
Sum of electronic and thermal Enthalpies= -234.395061
Sum of electronic and thermal Free Energies= -234.431749</pre>

'''8. Key information'''

 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Boat || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -231.54309304 a.u. || C2v
|}

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

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

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450924
| align="center" | -231.445295
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539540
| align="center" | -231.532567
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

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

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

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

= The Diels Alder Cycloaddition =

=== Diels Alder Reaction Between Cis-Butadiene and Ethylene ===
==== Optimising the Reactants ====
===== (a) Optimisation of cis-butadiene =====
'''1. Optimising cis butadiene using AM1 method'''

[[File:mh-cis-butadiene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cis-butadiene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cis-butadiene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
<pre> Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540843D-07
Optimization completed.
-- Stationary point found.</pre>
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cis-butadiene-opti-pointgroup.PNG]]

'''6. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cis-butadiene-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cis-butadiene-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''7. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cis-butadiene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.04879734 a.u. || C2v
|}

===== (b) Optimisation of ethylene =====
'''1. Optimising ethylene using AM1 method'''

[[File:mh-ethene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-ethene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-ethene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-2.644693D-09
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-ethene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Ethylene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02619024 a.u. || D2h
|}

==== Optimising the Transition Structure ====
===== (a) Optimisation of guess transition state =====
'''1. Optimising guess transition state using AM1 method'''

[[File:mh-cyclohexene-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess transition state was drawn as above by combining the optimised ethylene and butadiene structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the H-C-H bond angles. The optimised structure is shown below, which has 2.11929 Å bond lengths for the partially formed bonds.

[[File:mh-cyclohexene-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexene-transition-opti-re.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexene-transition-opti-sum-re.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000000 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-3.424099D-17
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-cyclohexene-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 956.25 cm-1. The corresponding vibrational mode is shown below, in which the C atoms of ethylene and the two terminal C atoms of butadiene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation. This is exactly what happens in the [4+2] cycloaddtion, that is, two or more C-C bonds form at the same time (i.e. a concerted process) in a 6-membered ring like system.

[[File:mh-cyclohexene-transition-opti-vibration.gif]]

'''7. Thermochemistry'''
<pre> Sum of electronic and zero-point Energies= 0.253275
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015</pre>

'''8. HOMO/LUMO visialisation'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-opti-HOMO.PNG|thumb|250px|HOMO-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-opti-LUMO.PNG|thumb|250px|LUMO-symmetric with respect to plane]]
|}

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.11165464 a.u. || Cs
|}

===== (b) IRC analysis of optimised transition state =====
'''1. Calculating minimum energy path from transition state'''
 
[[File:mh-cyclohexene-transition-IRC.gif|centre]]

As the reaction coordinate is not symmetrical in the Diels Alder cycloaddition, "both directions" is chosen for this IRC calculation. There are 87 intermediate geometries, which are connected together to show the geometric change following the calculated minimum energy path from reactant to product via the transition state. The structure of the last point of this IRC calculation is shown below.

'''2. File link'''
 
The IRC analysed file is linked to [[Media:mh-cyclohexene-transition-IRC-re.LOG| here]].

'''3. IRC plot'''

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-cyclohexene-transition-IRC-energy.PNG|thumb|250px|Total energy]]
! style="text-align: centre;"|[[Image:mh-cyclohexene-transition-irc-gradient.PNG|thumb|250px|RMS Gradient Norm]]
|}

As the IRC plot is shown above, the energy minimum is reached in this calculation because the RMS gradient reaches 0 in the end. Therefore no need to conduct further calculation. The general and symmetry information of the last point of this IRC calculation is given in the following.

'''4. General information'''
 
[[File:mh-cyclohexene-transition-IRC-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''5. Symmetry information'''
 
[[File:mh-cyclohexene-transition-IRC-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || IRC, both directions, calculate always, compute 100 points || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.01099166 a.u. || Cs
|}

===== (c) Reoptimisation of transition state using B3LYP/6-31G(d) =====
'''1. Optimising transition state using B3LYP/6-31G(d)'''
 
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DA TS OPT BERNY AM1 631GD.mol</uploadedFileContents>
</jmolApplet></jmol>

'''2. File link'''
 
The optimised file is linked to [[Media:DA TS OPT BERNY AM1 631GD.LOG| here]].

'''3. General information'''
 
[[File:DA TS OPT BERNY AM1 631gd info.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000496 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
Predicted change in Energy=-7.705534D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.386 -DE/DX = 0.0 !
! R2 R(1,6) 2.9004 -DE/DX = 0.0 !
! R3 R(1,7) 2.2725 -DE/DX = 0.0 !
! R4 R(1,9) 2.7536 -DE/DX = 0.0 !
! R5 R(1,10) 2.4251 -DE/DX = 0.0 !
! R6 R(1,15) 1.0842 -DE/DX = 0.0 !
! R7 R(1,16) 1.0863 -DE/DX = 0.0 !
! R8 R(2,3) 2.2725 -DE/DX = 0.0 !
! R9 R(2,4) 2.9004 -DE/DX = 0.0 !
! R10 R(2,11) 2.4251 -DE/DX = 0.0 !
! R11 R(2,12) 2.7536 -DE/DX = 0.0 !
! R12 R(2,13) 1.0842 -DE/DX = 0.0 !
! R13 R(2,14) 1.0863 -DE/DX = 0.0 !
! R14 R(3,4) 1.383 -DE/DX = 0.0 !
! R15 R(3,11) 1.084 -DE/DX = 0.0 !
! R16 R(3,12) 1.0873 -DE/DX = 0.0 !
! R17 R(3,13) 2.5399 -DE/DX = 0.0 !
! R18 R(3,14) 2.5323 -DE/DX = 0.0 !
! R19 R(4,5) 1.0891 -DE/DX = 0.0 !
! R20 R(4,6) 1.4072 -DE/DX = 0.0 !
! R21 R(6,7) 1.383 -DE/DX = 0.0 !
! R22 R(6,8) 1.0891 -DE/DX = 0.0 !
! R23 R(7,9) 1.0873 -DE/DX = 0.0 !
! R24 R(7,10) 1.084 -DE/DX = 0.0 !
! R25 R(7,15) 2.5399 -DE/DX = 0.0 !
! R26 R(7,16) 2.5323 -DE/DX = 0.0 !
! A1 A(2,1,6) 90.2098 -DE/DX = 0.0 !
! A2 A(2,1,7) 109.1164 -DE/DX = 0.0 !
! A3 A(2,1,9) 131.4998 -DE/DX = 0.0 !
! A4 A(2,1,10) 98.9089 -DE/DX = 0.0 !
! A5 A(2,1,15) 120.0522 -DE/DX = 0.0 !
! A6 A(2,1,16) 119.9852 -DE/DX = 0.0 !
! A7 A(6,1,9) 44.4899 -DE/DX = 0.0 !
! A8 A(6,1,10) 46.5393 -DE/DX = 0.0 !
! A9 A(6,1,15) 83.3596 -DE/DX = 0.0 !
! A10 A(6,1,16) 118.2474 -DE/DX = 0.0 !
! A11 A(9,1,10) 40.6754 -DE/DX = 0.0 !
! A12 A(9,1,15) 77.8409 -DE/DX = 0.0 !
! A13 A(9,1,16) 80.5628 -DE/DX = 0.0 !
! A14 A(10,1,15) 116.9474 -DE/DX = 0.0 !
! A15 A(10,1,16) 74.6439 -DE/DX = 0.0 !
! A16 A(15,1,16) 115.1638 -DE/DX = 0.0 !
! A17 A(1,2,3) 109.1165 -DE/DX = 0.0 !
! A18 A(1,2,4) 90.2099 -DE/DX = 0.0 !
! A19 A(1,2,11) 98.9089 -DE/DX = 0.0 !
! A20 A(1,2,12) 131.5 -DE/DX = 0.0 !
! A21 A(1,2,13) 120.0522 -DE/DX = 0.0 !
! A22 A(1,2,14) 119.9852 -DE/DX = 0.0 !
! A23 A(4,2,11) 46.5393 -DE/DX = 0.0 !
! A24 A(4,2,12) 44.49 -DE/DX = 0.0 !
! A25 A(4,2,13) 83.3596 -DE/DX = 0.0 !
! A26 A(4,2,14) 118.2474 -DE/DX = 0.0 !
! A27 A(11,2,12) 40.6755 -DE/DX = 0.0 !
! A28 A(11,2,13) 116.9475 -DE/DX = 0.0 !
! A29 A(11,2,14) 74.644 -DE/DX = 0.0 !
! A30 A(12,2,13) 77.8409 -DE/DX = 0.0 !
! A31 A(12,2,14) 80.5627 -DE/DX = 0.0 !
! A32 A(13,2,14) 115.1638 -DE/DX = 0.0 !
! A33 A(4,3,11) 120.6613 -DE/DX = 0.0 !
! A34 A(4,3,12) 120.0232 -DE/DX = 0.0 !
! A35 A(4,3,13) 94.0558 -DE/DX = 0.0 !
! A36 A(4,3,14) 127.3507 -DE/DX = 0.0 !
! A37 A(11,3,12) 114.4864 -DE/DX = 0.0 !
! A38 A(11,3,13) 109.2312 -DE/DX = 0.0 !
! A39 A(11,3,14) 69.5135 -DE/DX = 0.0 !
! A40 A(12,3,13) 88.6205 -DE/DX = 0.0 !
! A41 A(12,3,14) 91.9441 -DE/DX = 0.0 !
! A42 A(13,3,14) 42.3516 -DE/DX = 0.0 !
! A43 A(2,4,5) 121.3465 -DE/DX = 0.0 !
! A44 A(2,4,6) 89.7903 -DE/DX = 0.0 !
! A45 A(3,4,5) 118.6679 -DE/DX = 0.0 !
! A46 A(3,4,6) 122.0341 -DE/DX = 0.0 !
! A47 A(5,4,6) 117.9096 -DE/DX = 0.0 !
! A48 A(1,6,4) 89.7901 -DE/DX = 0.0 !
! A49 A(1,6,8) 121.3467 -DE/DX = 0.0 !
! A50 A(4,6,7) 122.0341 -DE/DX = 0.0 !
! A51 A(4,6,8) 117.9096 -DE/DX = 0.0 !
! A52 A(7,6,8) 118.6679 -DE/DX = 0.0 !
! A53 A(6,7,9) 120.0232 -DE/DX = 0.0 !
! A54 A(6,7,10) 120.6613 -DE/DX = 0.0 !
! A55 A(6,7,15) 94.0558 -DE/DX = 0.0 !
! A56 A(6,7,16) 127.3506 -DE/DX = 0.0 !
! A57 A(9,7,10) 114.4864 -DE/DX = 0.0 !
! A58 A(9,7,15) 88.6207 -DE/DX = 0.0 !
! A59 A(9,7,16) 91.9443 -DE/DX = 0.0 !
! A60 A(10,7,15) 109.2309 -DE/DX = 0.0 !
! A61 A(10,7,16) 69.5133 -DE/DX = 0.0 !
! A62 A(15,7,16) 42.3515 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -20.742 -DE/DX = 0.0 !
! D2 D(6,1,2,4) 0.0 -DE/DX = 0.0 !
! D3 D(6,1,2,11) -45.918 -DE/DX = 0.0 !
! D4 D(6,1,2,12) -18.3309 -DE/DX = 0.0 !
! D5 D(6,1,2,13) 82.445 -DE/DX = 0.0 !
! D6 D(6,1,2,14) -123.2664 -DE/DX = 0.0 !
! D7 D(7,1,2,3) -0.0001 -DE/DX = 0.0 !
! D8 D(7,1,2,4) 20.742 -DE/DX = 0.0 !
! D9 D(7,1,2,11) -25.1761 -DE/DX = 0.0 !
! D10 D(7,1,2,12) 2.4111 -DE/DX = 0.0 !
! D11 D(7,1,2,13) 103.1869 -DE/DX = 0.0 !
! D12 D(7,1,2,14) -102.5244 -DE/DX = 0.0 !
! D13 D(9,1,2,3) -2.4112 -DE/DX = 0.0 !
! D14 D(9,1,2,4) 18.3308 -DE/DX = 0.0 !
! D15 D(9,1,2,11) -27.5872 -DE/DX = 0.0 !
! D16 D(9,1,2,12) -0.0001 -DE/DX = 0.0 !
! D17 D(9,1,2,13) 100.7758 -DE/DX = 0.0 !
! D18 D(9,1,2,14) -104.9356 -DE/DX = 0.0 !
! D19 D(10,1,2,3) 25.176 -DE/DX = 0.0 !
! D20 D(10,1,2,4) 45.918 -DE/DX = 0.0 !
! D21 D(10,1,2,11) -0.0001 -DE/DX = 0.0 !
! D22 D(10,1,2,12) 27.5871 -DE/DX = 0.0 !
! D23 D(10,1,2,13) 128.3629 -DE/DX = 0.0 !
! D24 D(10,1,2,14) -77.3484 -DE/DX = 0.0 !
! D25 D(15,1,2,3) -103.1869 -DE/DX = 0.0 !
! D26 D(15,1,2,4) -82.4449 -DE/DX = 0.0 !
! D27 D(15,1,2,11) -128.3629 -DE/DX = 0.0 !
! D28 D(15,1,2,12) -100.7758 -DE/DX = 0.0 !
! D29 D(15,1,2,13) 0.0 -DE/DX = 0.0 !
! D30 D(15,1,2,14) 154.2887 -DE/DX = 0.0 !
! D31 D(16,1,2,3) 102.5243 -DE/DX = 0.0 !
! D32 D(16,1,2,4) 123.2663 -DE/DX = 0.0 !
! D33 D(16,1,2,11) 77.3483 -DE/DX = 0.0 !
! D34 D(16,1,2,12) 104.9354 -DE/DX = 0.0 !
! D35 D(16,1,2,13) -154.2888 -DE/DX = 0.0 !
! D36 D(16,1,2,14) -0.0001 -DE/DX = 0.0 !
! D37 D(2,1,6,4) 0.0 -DE/DX = 0.0 !
! D38 D(2,1,6,8) -123.0828 -DE/DX = 0.0 !
! D39 D(9,1,6,4) -160.3592 -DE/DX = 0.0 !
! D40 D(9,1,6,8) 76.5581 -DE/DX = 0.0 !
! D41 D(10,1,6,4) -102.1158 -DE/DX = 0.0 !
! D42 D(10,1,6,8) 134.8014 -DE/DX = 0.0 !
! D43 D(15,1,6,4) 120.2482 -DE/DX = 0.0 !
! D44 D(15,1,6,8) -2.8345 -DE/DX = 0.0 !
! D45 D(16,1,6,4) -124.7021 -DE/DX = 0.0 !
! D46 D(16,1,6,8) 112.2151 -DE/DX = 0.0 !
! D47 D(1,2,4,5) 123.0828 -DE/DX = 0.0 !
! D48 D(1,2,4,6) 0.0 -DE/DX = 0.0 !
! D49 D(11,2,4,5) -134.8015 -DE/DX = 0.0 !
! D50 D(11,2,4,6) 102.1157 -DE/DX = 0.0 !
! D51 D(12,2,4,5) -76.5581 -DE/DX = 0.0 !
! D52 D(12,2,4,6) 160.3591 -DE/DX = 0.0 !
! D53 D(13,2,4,5) 2.8345 -DE/DX = 0.0 !
! D54 D(13,2,4,6) -120.2482 -DE/DX = 0.0 !
! D55 D(14,2,4,5) -112.2151 -DE/DX = 0.0 !
! D56 D(14,2,4,6) 124.7022 -DE/DX = 0.0 !
! D57 D(11,3,4,5) -160.592 -DE/DX = 0.0 !
! D58 D(11,3,4,6) 33.1448 -DE/DX = 0.0 !
! D59 D(12,3,4,5) -6.5509 -DE/DX = 0.0 !
! D60 D(12,3,4,6) -172.8141 -DE/DX = 0.0 !
! D61 D(13,3,4,5) 84.1997 -DE/DX = 0.0 !
! D62 D(13,3,4,6) -82.0635 -DE/DX = 0.0 !
! D63 D(14,3,4,5) 112.8115 -DE/DX = 0.0 !
! D64 D(14,3,4,6) -53.4517 -DE/DX = 0.0 !
! D65 D(2,4,6,1) 0.0 -DE/DX = 0.0 !
! D66 D(2,4,6,7) -40.4359 -DE/DX = 0.0 !
! D67 D(2,4,6,8) 125.9267 -DE/DX = 0.0 !
! D68 D(3,4,6,1) 40.436 -DE/DX = 0.0 !
! D69 D(3,4,6,7) 0.0 -DE/DX = 0.0 !
! D70 D(3,4,6,8) 166.3627 -DE/DX = 0.0 !
! D71 D(5,4,6,1) -125.9267 -DE/DX = 0.0 !
! D72 D(5,4,6,7) -166.3626 -DE/DX = 0.0 !
! D73 D(5,4,6,8) 0.0001 -DE/DX = 0.0 !
! D74 D(4,6,7,9) 172.8141 -DE/DX = 0.0 !
! D75 D(4,6,7,10) -33.1446 -DE/DX = 0.0 !
! D76 D(4,6,7,15) 82.0633 -DE/DX = 0.0 !
! D77 D(4,6,7,16) 53.4515 -DE/DX = 0.0 !
! D78 D(8,6,7,9) 6.5509 -DE/DX = 0.0 !
! D79 D(8,6,7,10) 160.5921 -DE/DX = 0.0 !
! D80 D(8,6,7,15) -84.2 -DE/DX = 0.0 !
! D81 D(8,6,7,16) -112.8118 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 
Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:DA TS OPT BERNY AM1 631gd pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:DA TS OPT BERNY AM1 631gd vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 524.81 cm-1. The corresponding vibrational mode is shown below, and the motion is similar to that of the HF/3-21G optimised structure but slower.

[[File:DA TS OPT BERNY AM1 631gd vibration.gif]]

'''7. Thermochemistry'''
Sum of electronic and zero-point Energies= -234.403325
Sum of electronic and thermal Energies= -234.396907
Sum of electronic and thermal Enthalpies= -234.395963
Sum of electronic and thermal Free Energies= -234.432892

'''8. HOMO/LUMO visialisation'''
 
[[File:DA TS OPT BERNY AM1 631gd HOMOLUMO.png]]

'''9. Key information'''
 
{| class="wikitable" border="1"
! Subject !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Transition state || Optimisation to a TS (Berny), calculate the force constants once || Opt=NoEigen || B3LYP || 6-31G(d) || Default || -234.54389655 a.u. || Cs
|}

=== Diels Alder Reaction Between Cyclohexa-1,3-diene and Maleic Anhydride ===
==== Optimising the Reactants ====
===== (a) Optimisation of cyclohexa-1,3-diene =====
'''1. Optimising cyclohexa-1,3-diene using AM1 method'''

[[File:mh-cyclohexa-1-3-diene-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-cyclohexa-1-3-diene-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001024 0.001800 YES
RMS Displacement 0.000279 0.001200 YES
Predicted change in Energy=-2.196587D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-cyclohexa-1-3-diene-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Cyclohexa-1,3-diene || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || 0.02795816 a.u. || C2v
|}

===== (b) Optimisation of maleic anhydride =====
'''1. Optimising maleic anhydride using AM1 method'''

[[File:mh-maleic-anhydride-opti.PNG|thumb|centre|250px|Optimised structure]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-maleic-anhydride-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-maleic-anhydride-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000129 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.001415 0.001800 YES
RMS Displacement 0.000439 0.001200 YES
Predicted change in Energy=-3.063481D-07
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-maleic-anhydride-opti-pointgroup.PNG]]

'''6. Key information'''
 
{| class="wikitable" border="1"
! Molecule !! Job type !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Maleic anhydride || Optimisation to a minimum || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.12182404 a.u. || C2v
|}

==== Optimising the Exo and Endo Transition Structures ====
===== (a) Optimisation of Exo transition state =====
'''1. Optimising exo transition state using AM1 method'''

[[File:mh-exo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess exo transition state was drawn as above by combining the optimised cyclohexa-1,3-diene and maleic anhydride structures with two partially formed C-C bonds of 2.2 Å bond length and modifying the cyclohexa-1,3-diene into envelope structre. The optimised structure is shown below, which has 2.17078 Å bond lengths for the partially formed bonds.

[[File:mh-exo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised exo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-exo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-exo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000001 0.000060 YES
RMS Displacement 0.000000 0.000040 YES
Predicted change in Energy=-4.648033D-15
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-exo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-exo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 812.23 cm-1. The corresponding vibrational mode is shown below. Although the reactants different, the transition structure for reaction between cyclohexa-1,3-diene and maleic Anhydride has a similar vibrational motion as the transition state structure for reaction between cis-Butadiene and ethylene obtained earlier, that is, the two C atoms of maleic Anhydride and the two middle C atoms of cyclohexa-1,3-diene approach each other in a sychronised motion and facilitates two simultaneous C-C bonds formation.

[[File:mh-exo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre>Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144881
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.099118</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Exo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05041985 a.u. || Cs
|}

===== (b) Optimisation of Endo transition state =====
'''1. Optimising endo transition state using AM1 method'''

[[File:mh-endo-transition-guess.PNG|thumb|centre|250px|guessed structure]]

The guess endo transition state was drawn in a similar way as for exo transition state.

[[File:mh-endo-transition-opti.PNG|300px|thumb|centre|A GaussView image of a optimised endo transition state using AM1 method.]]

'''2. File link'''
 
The optimised file is linked to [[Media:mh-endo-transition-opti.LOG| here]].

'''3. General information'''
 
[[File:mh-endo-transition-opti-sum.PNG]]

The gradient is less than 0.001, which means the optimisation is complete.

'''4. Real output'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000009 0.000060 YES
RMS Displacement 0.000002 0.000040 YES
Predicted change in Energy=-1.103715D-12
Optimization completed.
-- Stationary point found.</pre>

Both force and displacement are converged, indicating the success of optimisation.

'''5. Symmetry information'''
 
[[File:mh-endo-transition-opti-pointgroup.PNG]]

'''6. Vibrational frequencies'''
 
[[File:mh-endo-transition-opti-vibfreq.PNG]]

As the above table is shown, there is only one imaginary frequency that has a magnitude of 806.40 cm-1. The corresponding vibrational mode is shown below, and the endo transition structure has a similar vibrational motion as the exo transition structure obtained earlier.

[[File:mh-endo-transition-opti-vibration.gif]]

'''7. Thermochemistry'''

<pre> Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350</pre>

'''8. Key information'''
 
{| class="wikitable" border="1"
! Transition state type !! Job type !! Additional keywords !! Method !! Basis set !! Memory limit !! Energy !! Point group
|-
| Endo || Optimisation to a TS (Berny), calculate the force constants always || Opt=NoEigen || Semi-empirical molecular orbital, AM1 || ZDO || Default || -0.05150480 a.u. || Cs
|}

===== (c) HOMO visialisation of exo and endo transition state=====

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:mh-exo-transition-opti-HOMO.PNG|thumb|250px|HOMO of exo transition state-antisymmetric with respect to plane]]
! style="text-align: centre;"|[[Image:mh-endo-transition-opti-HOMO.PNG|thumb|250px|HOMO of endo transition state-antisymmetric with respect to plane]]
|}