2012-03-22T20:16:56Z

Hgl09: /* Transition state */

Module 3: Transition States and Reactivity

= Introduction =

Apart from studying the structures and bonding of molecules, computational chemistry is also a powerful tool used to study the transition states and reactivity of molecules. In this modules, the transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition are characterised using orbital-based methods. The reaction paths and barrier heights are calculated as well.

= The Cope Rearrangement =

The [3,3]-sigmatropic rearrangement undergoes via the following reaction scheme:

[[File: Hgl_Reaction_schemecope.png|300px]]

There are two possible transition structures, a ''chair'' and a ''boat''. The ''boat'' is known to have a higher energy than the ''chair''.<ref>O. Wiest, K.A. Black and K.N. Houk, ''J. Am. Chem. Soc.'', '''1994''', 116, 10336-10337 {{DOI|10.1021/ja00101a078}}</ref> In this experiment, such activation energies and enthalpies are calculated using Gaussian09W.

== Optimising the Reactants and Products ==

=== Optimisation of 1,5-hexadiene ===

The anti structure was optimized at the HF/3-21G level with %mem=250MB. The structure obtained after optimisation has a point group of C2. A gauche structure was created by adjusting the dihedral angles of the optimised anti structure, submitted with the same setting used for the anti one. The point group obtained is also C2. The summary of optimisation of both structures are shown below. It would be expected the anti structure has lower energy than that of the gauche one since there are less steric effect.

{|
|[[File: Hgl_Anti_opt.png|thumb|250px|optimisation of ''anti1'' linkage structure]]

|[[File: Hgl_250mb_Gauche_opt.png|thumb|250px|optimisation of ''gauche2'' linkage structure]]
|}

Referring to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1], it is found that the anti structure obtained is ''anti1'' while the gauche structure obtained is ''gauche2''.

{| border="3" style="margin-left: 3em;"
|+ Optimisation of 1,5-hexadiene of '''C2''' symmetry
|-
! scope="col" | Structures
! scope="col" | Total Enegy (a.u.)
! scope="col" | Energy (kJ/mol)
|-
! scope="row" | anti1
<jmol>
<jmolApplet>
<title>anti1</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Anti1_optsturcture.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69260
| -145389.3
|-
! scope="row" | gauche2
<jmol>
<jmolApplet>
<title>gauche2</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Gauche2_opt.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69167
| -145388.7
|}

The results do agree with the prediction. Since the four centre carbons on anti1 all have antiperiplanar confomations, it was predicted to be the one having the lowest energies. To test my hypothesis, several ''anti'' and ''gauche'' structures were tested and the results are all summarized in the Table 1.

{| class="wikitable" border="1"
|+ Table 1: Optimisation of different conformers of 1,5-hexadiene
! Conformers !! Total Energy(a.u)!! Point Group!! Relative Energy (kcal/mol)!! References
|-
| <jmolFile text=anti1>Hgl_Anti1_optsturcture.mol</jmolFile> || -231.69260 || C2 || 0.04 || {{DOI|10042/to-57902}}
|-
| <jmolFile text=anti2>Hgl hexadiene Anti2.mol</jmolFile> || -231.69254 || Ci || 0.08 || {{DOI|10042/to-58114}}
|-
| <jmolFile text=anti3>Hgl hexanedieneAnti3.mol</jmolFile> || -231.68907 || C2h || 2.25 || {{DOI|10042/to-57929}}
|-
| <jmolFile text=anti4>Hgl hexadiene Anti4.mol</jmolFile> || -231.69097 || C1 || 1.06 || {{DOI|10042/to-58343}}
|-
| <jmolFile text=gauche1>Hgl_Gauche1.mol</jmolFile> || -231.68772 || C2 || 3.10 || {{DOI|10042/to-57930}}
|-
| <jmolFile text=gauche2>Hgl_Gauche2_opt.mol</jmolFile> || -231.69167 || C2 || 0.62 || {{DOI|10042/to-57903}}
|-
| <jmolFile text=gauche3>Hgl_Gauche3.mol</jmolFile> || -231.69266 || C1 || 0.00 || {{DOI|10042/to-58234}}
|-
| <jmolFile text=gauche4>Hgl_Gauche4.mol</jmolFile> || -231.69153 || C2 || 0.71 || {{DOI|10042/to-58118}}
|-
| <jmolFile text=gauche5>Hgl_Gauche5.mol</jmolFile> || -231.68962 || C1 || 1.91 || {{DOI|10042/to-58543}}
|-
| <jmolFile text=gauche6>Hgl_Gauche6.mol</jmolFile> || -231.68916 || C1 || 2.20 || {{DOI|10042/to-58544}}
|}

Surprisingly, gauche3 turns out to be the one having the lowest energy and the predicted structure anti1 is the 2nd lowest energy among the tested structures. However, the difference between them is not significant. A further test was carried out using B3LYP/6-31G* levels. The results obtained do agree with the prediction. The results are shown in Table 2.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | Conformers
! scope="col" | Total Enegy (a.u.)
! scope="col" | Relative Energy (kcal/mol)
! scope="col" | Point Group
! scope="col" | DOI
|-
! scope="row" | anti1
| -234.61179
| 0.00
| C2
| {{DOI|10042/to-58564}}
|-
! scope="row" | gauche3
| -234.61133
| 0.29
| C2
| {{DOI|10042/to-58562}}
|}

After optimisation at higher levels, anti1 has the lowest energy than that of gauche3, which agrees with my prediction. However, the high stability of gauche3 is due to the stabilisation resulted from overlap of the C=C π orbital with the C-H σ orbital<ref>A. Spivey, Lec 1, {{DOI|http://www.ch.ic.ac.uk/spivey/teaching/org3stereoelectronics/lecture11112.pdf}}</ref>, dominant over the steric repulsion within the structure.

=== Ci anti2 conformer ===

==== Optimisation of Ci anti2 conformer ====

Ci anti2 of 1,5-hexadiene was also optimised at the B3LYP/6-31G*. The final structures are compared in Table 3. The structures are symmetrical and therefore only half of the bond lengths and dihedral angles are reported.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | [[File: Hgl_Anti2_labelled.png|anti2 Conformer]]
! scope="col" | Total Enegy (a.u.)
! scope="col" | Point Group
! scope="col" | Bond Length (Å)
! scope="col" | DOI
|-
! scope="row" | anti2 optimised at HF/3-21G
| -231.69254
| Ci
| C(14)=C(12) 1.32; C(12)-C(9) 1.51; C(9)-C(6)1.55; C(14)-H(15) 1.07; C(12)-H(13) 1.08; C(9)-H(10) 1.09
| {{DOI|10042/to-58114}}
|-
! scope="row" | anti2 optimised at B3LYP/6-31G*
| -234.61171
| Ci
|C(14)=C(12) 1.33; C(12)-C(9) 1.50; C(9)-C(6)1.55; C(14)-H(15) 1.09; C(12)-H(13) 1.09; C(9)-H(10) 1.10
|{{DOI|10042/to-58419}}
|}

The C=C double bonds become longer and the C-C bonds are shorted after optimisating at the higher DFT/6-31G*. The difference between the enegy is about 2.9 a.u. which is equivalent to 7614kJ/mol. The overall geometry roughly stays the same.

==== Frequency Analysis ====

A frequency calculation was submitted to SCAN using the optimised anti2 conformers obtained at B3LYP/6-31G*. All vibrational frequencies obtained are real and positive. In addition, another frequency calculation was carried at 0K by setting the temperature at 0.00001K and pressure at 1 atm. The results are shown below. It is found that at absolute zero temperature, all four sums are the same. The sum of electronic and zero-point energies of the one at 298.15K roughly agrees with the one obtained at 0K.

{| class="wikitable" border="1"
|+ Frequency Analysis of anti2 conformer
! !!Frequency analysis at 298.15K !! Frequency analysis at 0K
|-
| IR spectrum|| [[File:Hgl_Anti2_ir_298.15.png|300px]]|| [[File:Hgl_Anti2_ir_ok.png|300px]]
|-
| Sum of electronic and zero-point energies (E=Eelec+ZPE) (a.u.)|| -234.469204|| -234.468766
|-
| Sum of electronic and thermal energies (E=E+Evib+ Erot+Etrans) (a.u.)|| -234.461857|| -234.468766
|-
| Sum of electronic and thermal enthalpies (H=E+RT) (a.u.)|| -234.460913|| -234.468766
|-
| Sum of electronic and thermal free energies (G=H-TS) (a.u.)|| -234.50077|| -234.468766
|-
| DOI||{{DOI|10042/to-58427}}|| {{DOI|10042/to-58598}}
|}

== Optimizing the ''Chair'' and ''Boat'' Transition Structures ==

In this section, the ''chair'' and ''boat'' transition structure optimisations for the Cope rearrangement were set up by
#computing the force constants at the beginning of the calculation;
#using the redundant coordinate editor;
#using QST2.

IRC(Intrinisic Reaction Coordinate) of both structures were run and the activation energies for the rearrangement via both transition structures were obtained.

=== Chair Transition State ===
An <jmolFile text=allyl fragement>Hgl_Gauche2_opt.mol</jmolFile> was created using GaussView 5.0. It was optimised using the HF/3-21G level of theory. The chair transition state was created using two of such fragment, the distance between the terminal ends of the fragments was set to 2.2Å. The ''chair'' structure was then optimised by using the methoeds mentioned in the previous section.

* Chair(b): Optimisating by Computing the force constants at the beginning of the calculation
The created ''chair'' transition states was optimised to a '''TS(Berny)''' by calculating the force constants '''once''' with ''Opt=NoEigen'' at the additional keyword box and a frequency calculation was also included. The calculated structure is a C2h ''chair''. The terminal ends of the two fragments are 2.02Å apart. In the frequency analysis, an imaginary frequency is found at -818cm-1, which confirms the existence of the transition state. The animated vibration is shown below.

[[File: Hgl_Chair_ts_img_vib.gif|thumb|300px|imaginary vibration of the chair transition structure]]

* Chair(d): Optimisaing using the redundant coordinate editor
The tranistion structure was optimised again using the frozen coordinate methods. The distances between the terminal C ends were ''freezed'' to 2.2Å and was optimised to a minimum with ''Opt=ModRedundant'' included in the input file. The optimised structure (chair (c)) looks similar to the one obtained from the previous section. Since the terminal distance was freezed, the distance between them is still 2.2Å. A further optimisation was set up using '''Redundant Coord Editor'''. The Bond was set to ''Derivative'' and a transition state optimised was set up with calculation of the force constant set to '''Never'''. The obtained structure looks again the same as the ones obtained in the previous section, and the distance between the terminal C ends is also the same, 2.02Å.

{| class="wikitable" border="1"
|+ Optimisation of ''chair'' transition state
! Optimisation methods!! Optimisating by Computing the force constants at the beginning of the calculation!! Optimisaing using the redundant coordinate editor (freezed bond length)!!Optimisaing using the redundant coordinate editor (derivative bond length)
|-
| Energy (a.u.) || -231.61932|| -231.61519|| -231.61932
|-
| Terminal C ends distance(Å) || 2.02|| 2.20|| 2.02
|-
| Jmol || <jmolFile text=chair(b)>Hgl_Chair_opt_b.mol</jmolFile>|| <jmolFile text=chair(c)>Hgl_Chair_opt_c.mol</jmolFile>|| <jmolFile text=chair(d)>Hgl_Chair_opt_d.mol</jmolFile>
|-
| DOI || {{DOI|10042/to-58130}}|| {{DOI|10042/to-58129}}|| {{DOI|10042/to-58136}}
|}

=== Boat Transition State ===

The ''boat'' transition state was optimised using QST2 method. The reactant molecule used was anti2 conformer. Two molecules were set up in the same window and the two structures were oriented following the lab script. The atoms were labelled to have the atoms on the product all match the reactant molecule.

{|
|[[File: Hgl_Boat_scheme.png|400px]]
|[[File:Hgl_Boat_qst2_fail.png|400px]]
|}

The structure was then submitted to scan for transition state optimisation and a frequency calculation was also included. The script used was shown below:
---------------------------------------------------
# opt=(calcfc,qst2) freq hf/3-21g geom=connectivity
---------------------------------------------------
However, the optimisation failed as the sturcture obtained looks more like a dissociated ''chair'' transition state. A similar imaginary vibration to the chair structure is also found at -818cm-1, which further confirms the structure obtained is the chair transition state.
{|
![[File:HGL_Boat_qst2_FAIL_1.png|thumb|middle|200px|failed boat transition structure optimisation]]
![[File: Hgl_Boat_qst2.png|thumb|middle|400px|modified structure for boat optimisation]]
|}

The original input file was then modified to make it look as close to the boat transition state as possible. Both the reactant and product had the central C-C-C-C- dihedral angle set to 0o, with the inside C-C-C reduced to 100o.

{| class="wikitable" border="1"
|+ Optimisation of Boat transition state
! Summary !! [[File:Hgl_Boat_qst2_summary.png|300px]]
|-
| Terminal C ends distance || 2.14
|-
|Imiginary vibration at -840cm-1|| [[Image:Hgl_Boat_vib.gif|thumb|300px|click to start it]]
|-
| DOI || {{DOI|10042/to-58156}}
|}

=== Intrinsic Reaction Coordinate (IRC) Analysis ===

Intrinsic Reaction Coordinate(IRC) is a method providing information on the minimum energy path from the transition structure down to its local minimum on a potential energy surface. The IRC was calculated using the optimised transition structures from the previous sections. As the reaction coordinate is symmetrical, only forward direction was chose to be computed and the force constant was calculated once with number of points along the IRC set to 50.

It was found that the IRC terminated at step 21 but it hadn't reached a minimum. The final structure obtained looks more like the structure used for the boat tranistion state optimisation. The total energy is -231.687731a.u.
{| class="wikitable" border="1"
|+ IRC calculation
! Resulted conformer !! IRC Diagram!! RMS Gradient
|-
| [[File:Hgl_Chair_irc.gif|200px]]|| [[File:Hgl Chair irc energy.png|300px]]|| [[File:Hgl_Chair_irc_rms.png|300px]]
|}
{{DOI|10042/to-58735}}

Three different methods were then used to make the IRC reach a minimum geometry.

(i)''Take the last step of IRC and run a normal minimisation''

A normal optimisation to a minimum was set up using the final structure obtained from the previous IRC calculation. The calculation finished very fast. However, the structure obtained is the same as gauche2 with the same total energy, -231.69167 a.u and point group C2. This indicates the ''chair'' transition structure leads to the gauche2 conformer.

(ii)''Restart the IRC and set the no. of points along the IRC 100''

The same result was obtained as running the IRC with the no. of points along the IRC set to 50. Therefore, this method isn't much improvement either.

(iii)''Redo the IRC and compute the force constants at each step''

The force constant was set to '''always''' while the other settings were kept the same as the initial IRC calculation. The results obtained has the similar total energy as the one obtained using (i), -231.69166 a.u. This is again confirms that the ''chair'' transition state leads to gauche2 conformer. This method terminates at step 47.

{| class="wikitable" border="1"
|+ IRC calculation using different methods
! Methods !!(i) !! (ii) !! (iii)
|-
| Animation|| [[File:Hgl_Chair_irc_1.gif|200px]] || [[File:Hgl_Chair_irc_2.gif|200px]] || [[File:Hgl_Chair_irc_3.gif|200px]]
|-
| Total Energy (a.u) || -231.69167 || -231.68514 || -231.69166
|-
| IRC Total Energy Graph|| [[File:Hgl_Chair_irc_i_energy.png|300px]] || [[File: Hgl_Chair_irc_ii_energy.png|300px]] || [[File: Hgl_Chair_irc_iii_energy.png|300px]]
|-
| IRC RMS|| [[File:Hgl_Chair_irc_i_rms.png|300px]] || [[File:Hgl_Chair_irc_ii_rms.png|300px]] || [[File:Hgl_Chair_irc_iii_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58745}} || {{DOI|10042/to-58747}} || {{DOI|10042/to-58748}}
|}

In conclusion, it is found that method (iii) could be the best choice among the three as it only requires one IRC calculation which would have reached the minimum geometry. Therefore, the IRC calculation of the ''boat'' transition state was carried out using method(iii). The structure obtained at the final step is a gauche conformer of point group C1.

{| class="wikitable" border="1"
|+ IRC calculation of ''boat'' transition state
! Animation !! [[File:Hgl_Boat_irc.gif|200px]]
|-
| Total Energy (a.u.) || -231.68528
|-
| IRC Total Energy Graph || [[File: Hgl_Boat_irc_energy.png|300px]]
|-
| IRC RMS || [[File: Hgl_Boat_irc_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58238}}
|}

=== Activation Energies ===

Both ''chair'' and ''boat'' transition structures were optimised at B3LYP/6-31G* levle of theory using the HF/3-21G optimised structures. The activation energy is obtained by finding the difference between the reactants and transition states with the corresponding calculating methods. The methods used are listed below. Since the sum of electronic and zero-point energy at different temperatures roughly agrees, the sum was obtained from the 298.15K .log file.

{| class="wikitable" border="1"
|+ Optimisation of transition states
! Transition States!! Optimisation Methods !! Point Groups !! Electronic Energy (a.u)!! Sum of electronic and zero-point energies at 298.15K(a.u)!! Sum of electronic and thermal energies at 0K(a.u.)!! Terminal C ends distance (Å) !! Activation Energies at 298.15K(kcal/mol)!! Activation Energies at 0K(kcal/mol)!!DOI
|-
| Reactant (anti2) || HF/3-21G|| C2v ||-231.69254|| -231.52681|| -231.53907|| N/A|| N/A|| N/A || 0K {{DOI|10042/to-59019}};278.15K {{DOI|10042/to-59025}}
|-
| Reactant (anti2) || B31YP/6-31G*|| C2v ||-234.61171|| -234.46143|| -234.46877|| N/A|| N/A||N/A || 0K {{DOI|10042/to-58598}}; 278.15K {{DOI|10042/to-58556}}
|-
| chair || HF/3-21G || C2h || -231.61932|| -231.46132|| -231.46667|| 2.02 || 41.1|| 45.4|| 278.15K {{DOI|10042/to-58969}}
|-
| chair || B31YP/6-31G*|| C2h|| -234.55698|| -234.40901|| -234.41493|| 1.97 || 32.9|| 33.8|| 278.15K {{DOI|10042/to-58414}}
|-
| boat || HF/3-21G || C2v || -231.60280|| -231.44530|| -231.45093|| 2.14 || 51.1|| 46.5|| 278.15K {{DOI|10042/to-58972}}
|-
| boat || B31YP/6-31G*|| C2v || -234.54309||-234.39601||-234.40234|| 2.21|| 41.1|| 41.7|| 278.15K{{DOI|10042/to-59053}}
|}

As seen in the above table, the chair transition state has a lower activation energy than the boat one, which indicates chair transition state pathway would be more favoured in the Cope rearrangement. The experimental activation enegies are 33.5±0.5cal/mol via the chair transition state and 44.7±2.0kcal/mol.<ref> Mod3:phy https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3</ref> The computational results using DFT/6-31G* roughly agrees with it.

= Diels Alder Cycloaddition =

Diels Alder reaction is a pericyclic cycloaddition, occuring between a conjugated diene and a dienophile, involving 4π electrons from the diene and 2π electrons from dienophile. The reaction is driven by the formation of two new σ bonds. An aromatic transition state of six delocalised π electrons is formed. <ref>J. Claden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, 2001, pp905-906 ISBN: 978-0-19-850346-0</ref><ref>Diels Alder Reaction, http://www.organic-chemistry.org/namedreactions/diels-alder-reaction.shtm</ref> The HOMO and LUMO of the same symmetry interacts with each other, forming two new σ orbitals, which usually have lower energies than those of the dienophiles.

{|
|[[File:HGL_CYCLOHEXAENE_HOMO_LUMO.png|thumb|middle|250px|Cycloaddition MO interpretation]]
|}

In this section, the transition states of two π4s+π2s reaction are calculated, starting with AM1/semi-empricial level.

== Diels Alder reaction between ethylene and butadiene ==
Cis-butadiene is the diene and ethylene is the dienophile in the Diels Alder reaction. The reaction scheme is shown below.

{|
|[[File: Hgl_Diels_alder_scheme_1.png|thumb|350px|Diels Alder reaction between ethylene and butadiene]]
|}

=== cis butadiene and ethylene MO symmetry determinations ===

Both reactants were optimised at AM1 semi-empirical level, using Gaussian09W.

{| class="wikitable" border="1"
|+ Optimisation of cis-butadiene
! Molecules!!Total Energy (a.u) !! HOMO (a.u)!! LUMO (a.u)!!C=C Bond Lengths (Å)|| C-C Bond Length (Å)!!.log
|-
| Cis-butadiene|| 0.048797|| [[File:Hgl_Cis-butadiene_homo.png|thumb|250px| -0.34381(Symmetry=a)]]|| [[File: Hgl_Cis-butadiene_lumo.png|thumb|250px| 0.01707(Symmetry=s)]]|| 1.34||1.45||[[File:Hgl_CISBUTADIENE_OPT.LOG]]
|-
| Ethylene|| 0.02619|| [[File:Hgl_Ethylene_homo.png|thumb|250px| -0.38775(Symmetry=s)]]||[[File:Hgl_Ethylene_lumo.png|thumb|250px|0.05283(Symmetry=a)]]||1.33|| n/a||[[File:Hgl_ethylene_OPT.LOG]]
|}

It can be clearly seen the LUMOs and HOMOs are formed from p-orbital overlapping, forming π bonds. The HOMO and LUMO of the diene are π2 and π3* orbitals respectively<ref> Prof. H. Rzepa, Pericyclic theory, http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> while the HOMO and LUMO of the ethylene are the π and π* orbitals. The HOMO of the cis-butadiene has the same symmetry as the LUMO of ethylene, both antisymmetrical whereas the LUMO of the cis-butadiene and HOMO of the ethylene are both symmetrical. Therefore, the orbitals of the same symmetry can interact with each other and the reaction is allowed. Both the HOMO and LUMO of cis-butadiene have the lower energies. Thus, the energies of new σ bond orbitals formed decreases relative to the ones of ethylene.<ref>Molecular Orbitals In Conjugated System, http://www.chem.ucsb.edu/~kalju/chem109C/DielsAlder.html</ref>

=== Transition state ===

The transition state was set up using the optimised cis-butadiene and ethylene structures. It was first guessed using the redundant coord editor method and was then optimised to a transition state (''TS Berny'') at AM1-semiexpirical level. The distance between the C atoms where the two newly formed σ bonds form was froze to 2.2Å to start the optimisation. A frequency calculation was also carried out.
{| class="wikitable" border="1"
|+ Optimisation of Transition States
! Methods!! Freeze Coordinate (2.2Å) !! Freeze Coordinate (Derivative) !! TS(Berny) opt at semi-emprical/AM1
|-
| Total Energies (a.u) || 0.10745|| 0.11166|| 0.11165
|-
| Point Groups || Cs|| Cs|| Cs
|-
| Partyly formed C-C Distance (Å) || 2.20|| 2.12|| 2.12
|-
| Diene C-C Bond Length (Å)|| 1.42|| 1.40||1.40
|-
| Diene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| Ethylene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| DOI || {{DOI|10042/to-59109}}|| {{DOI|10042/to-59116}}|| {{DOI|10042/to-59121}}
|}

At the transition state, the C=C bond of both reactants get longer as when the two new σ bonds are forming at these positions, electrons transferring from the π orbitals into the corresponding LUMO and HOMO as mentioned above. An imaginary vibration is found in the frequency analysis, which confirms the transition state has been found and π electrons transferred in a concerted stereospecific fashion.

{| class="wikitable" border="1"
|+ Imiaginary and the lowest positive Vibration
! wavelength (cm-1) !! Animation!! Description
|-
| -956|| [[File:Hgl_cyclehexene_ts_2,4vib.gif|250px]]|| Synchronous movement of both fragments towards each other
|-
| 142|| [[File:Hgl_Lowest_positive_cyclohexene_vib.gif|250px]]|| Synchronous rocking of both fragments
|}

{| class="wikitable" border="1"
|+ Tranistion MO Analysis
! MOs!! HOMO !! LUMO
|-
| MO Images || [[File:HGL_CYCLOHEXENE_TS_HOMO.png|thumb|250px|symmetry=a]]|| [[File:HGL_CYCLOHEXENE_TS_LUMO.png|thumb|250px|symmetry=s]]
|-
| MO energies (a.u) || -0.32394|| 0.02315
|-
| Symmetries || Antisymmetric || Symmetrical
|}

The HOMO and LUMO of the transition states agrees with the prediction mentioned at the reactants MO sections. The electrons are transferred from the π orbitals which is the HOMO of one fragment into the π* which is the LUMO of the other fragment, forming two new σ orbitals which can be seen at the HOMO and having antisymmetric symmetry.<ref>

=== IRC ===
The IRC calculated at AM1/semi-emprical level further confirms the completion of finding the transition state. The final step structure has a symmetry of Cs.

{|
|[[File: Hgl_Irc_cyclohexene_ts.gif|thumb|250px|animation of IRC]]
|[[File: Hgl_Irc_cyclohexene.png|thumb|400px| IRC energy graph]]
|}

{{DOI|10042/to-58843}}

== Regioselectivity of the Diels Alder Reaction between Cyclohexa-1,3-diene and maleic anhydride==
There are two possible products in the Diels Alder reaction between cyclic diene and dienophile, ''endo'' and ''exo'' adducts. In this section, the transition states formed between cyclohexa-1,3-diene and maleic anhydride were tested to study the kinetics of the reaction.
{|
|[[File:Hgl_DIELS_ALDER_SCHEME_2.png|thumb|350px|Diels Alder reaction between cyclohexa-1,3-diene and maleic anhydride]]
|}

=== MO Analysis ===
Again, both cyclohexa-1,3-diene and maleic anhydride structures were optimised at AM1 semi-empirical level before starting any transition state calculation.
{| class="wikitable" border="1"
|+ Optimisation
! Molecules!! Total Energy (a.u.) !! HOMO(a.u.)!! LUMO(a.u)!!.log
|-
| Cyclohexa-1,3-diene || 0.02771|| [[File:Hgl_1,3cyclohexadiene_homo.png|thumb|250px|-0.32194(Symmetry=a)]]|| [[File:Hgl_1,3cyclohexadiene_lumo.png|thumb|250px|0.01680(Symmetry=s)]]|| {{DOI|10042/to-59077}}
|-
| Maleic Anhydride || -0.12182|| [[File:Hgl_Maleic_anhydride_homo.png|thumb|250px|-0.44187(Symmetry=s)]]||[[File:Hgl_Maleic_anhydride_lumo.png|thumb|250px|-0.05949(Symmetry=a)]]|| [[File:Hgl_MALEIC_ANHYDRIDE.LOG]]
|}

Both HOMO and LUMO of maleic anhydride have negative energies, resulting from the presence of more electronegative O atoms. The lower energy of LUMO enables better orbital overlapping with the HOMO of diene. <ref>''Zeolite Characterization and Catalysis: a Tutorial (google ebook)'', pp309 http://books.google.co.uk/books?id=UobhZh216WkC&pg=PA309&lpg=PA309&dq=homo+maleic+anhydride+diels+alder&source=bl&ots=pbb1sW5nSv&sig=eEpKj8gcNSJvVJhwZA4EKIGJBVM&hl=en&sa=X&ei=YEhrT6OMEMix0AWosaDBBg&ved=0CFQQ6AEwCTgK#v=onepage&q=homo%20maleic%20anhydride%20diels%20alder&f=false</ref>

=== Transition State ===
The transition states were set up by using the optimised maleic anhydride and cyclohexa-1,3-diene. Both structures were optimised using redundant coord editor method. The structures obtained were then optimised further using AM1/semi-emprical to TS(Berny) and frequency analysis were included as well. The partyly forming σ bonds were set to 2.2Å at the beginning of the freeze coordinate optimisation.The optimisation results are tabulated.

{| class="wikitable" border="1"
|+ Transition States Optimisation
! !!Endo Adduct !! Endo Adduct!! Exo Adduct!! Exo Adduct
|-
|Methods|| Redundant Coor Editor|| TS(Berny)|| Redundant Coor Editor|| TS(Berny)
|-
| Final structures|| [[File:Hgl_Endo_freeze.png|200px]] || [[File:Hgl_Endo_tsberny.png|200px]]||[[File:Hgl_Exo_freeze.png|200px]]|| [[File:Hgl_Exo_tsberny.png|200px]]
|-
| Total Energies (a.u)|| -0.06945|| -0.05150|| -0.06959|| -0.05042
|-
| Imaginary Vibration (cm-1)|| n/a|| -806|| n/a|| -812
|-
| Partly Forming σ C-C Bond Length (Å)|| 2.00|| 2.16 || 2.00|| 2.17
|-
| Diene C=C Bond (Å)|| 1.50|| 1.39|| 1.45|| 1.39
|-
| Diene C-C Bond (Å)|| 1.53|| 1.40|| 1.36|| 1.40
|-
| Anhydride C=C Bond (Å) || 1.47|| 1.41|| 1.47|| 1.41
|-
|DOI||{{DOI|10042/to-58705}}||{{DOI|10042/to-58708}}|| {{DOI|10042/to-58714}}|| {{DOI|10042/to-58719}}
|}

All the structures obtained have the same point group: Cs. By studying the imaginary vibrations of both, it is confirmed that the transition structures have been found.

Both endo and exo products were optimised at AM1/semi-emprical level. By studying into the log file, the following data can be obtained.<ref>http://www.chem.ucsb.edu/~kalju/chem111/public/qm_ts_hcn_hnc.html</ref>

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Total Energy (a.u)!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!!Sum of electronic and thermal free energies(a.u.)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!!ΔG(kcal/mol)!! DOI
|-
| Maleic Anhydride|| -0.05819|| -0.06335|| -0.05819|| -0.09250||||||||||||{{DOI|10042/to-59151}}
|-
| Cyclo-1,3-diene|| 0.02771|| 0.15250|| 0.15773|| 0.12449||||||||||||{{DOI|10042/to-59152}}
|-
| Reactants Total|| -0.03048|| 0.08915|| 0.09954|| 0.03199||||||||||||n/a
|-
| Endo TS|| -0.05150|| 0.13349|| 0.14368|| 0.09735|| 27.8|| 27.7||||||||{{DOI|10042/to-58708}}
|-
| Endo Product|| -0.16017|| 0.03146|| 0.04046|| -0.00316|| || ||-36.2|| -37.1|| -22.1||{{DOI|10042/to-59146}}
|-
| Exo TS ||-0.05042|| 0.13488|| 0.14488|| 0.09912|| 29.7|| 28.5|| ||||||{{DOI|10042/to-58719}}
|-
| Exo Product|| -0.15991|| 0.03170|| 0.04068|| -0.00288|| || || -36.1|| -37.0|| -62.9||{{DOI|10042/to-59147}}
|}

As found in the Cope rearrangement, the results obtained using DFT/6-31g* method are more accurately. i.e. the optimisation was then carried out at DFT/6-31G* level.

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Electronic Energy!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!! Sum of electronic and thermal free energies (a.u)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!! ΔG(a.u)!! DOI
|-
| Maleic Anhydride|| -379.28954|| -379.23366|| -379.22847|| -379.26273||||||||||||{{DOI|10042/to-59155}}
|-
| Cyclo-1,3-diene|| -233.41891|| -233.29610|| -233.29092|| -233.32370||||||||||||{{DOI|10042/to-59154}}
|-
| Reactants Total|| -612.70845|| -612.52976|| -612.51939|| -612.58643||||||||||||n/a
|-
| Endo TS|| -612.68340|| -612.50214|| -612.49179|| -612.53833|| 17.3|| 17.3||||||||{{DOI|10042/to-58758}}
|-
| Endo Product|| -612.75829|| -612.57207|| -612.56261|| -612.60718|| || || -26.5|| -27.1|| -13.0||{{DOI|10042/to-59157}}
|-
| Exo TS || -612.67931|| -612.49801|| -612.48766|| -612.53426|| 19.3|| 19.9|||| ||||{{DOI|10042/to-58757}}
|-
| Exo Product|| -612.75579|| -612.56938|| -612.55998|| -612.60428|| || || -24.9|| -25.5|| -11.2||{{DOI|10042/to-59156}}
|}

The results obtained using both methods exhibit the same trend: the endo transition state has the lower activation energy, which means it is the endo product is the kinetic product. i.e., the exo product is thermodynamic product.

=== Bonding interaction and Secondary Orbital Overlap ===

{| class="wikitable" border="1"
|+ MO Analysis
! MOs !! HOMO-1!! HOMO!! LUMO!! LUMO+1!! Energies
|-
| Exo Adduct || [[File:Hgl_Exo_homo-1.png|150px]]|| [[File:Hgl-Exo_homo.png|150px]]|| [[File:Hgl_Exo_lumo.png|150px]]||[[File:Hgl_Exo_lumo+1.png|150px]]||[[File:Hgl_Exo_energy.png|150px]]
|-
| Endo Adduct || [[File:Hgl_Endo_homo-1.png|150px]]|| [[File:Hgl_Endo_homo.png|150px]]||[[File:Hgl_Endo_lumo.png|150px]]||[[File:Hgl_Endo_lumo+1.png|150px]]||[[File:Hgl_Endo_energy.png|150px]]
|}

It can be clearly seen that the endo adduct MOs have lower energy than those of exo adduct.

The endo transition has the lower energy as a result of secondary orbital overlap.<ref>T.L. Gilchrist, R.C. Storr, ''Organic Reactions and Orbital Symmetry'', pp119 ISBN:9780521293365</ref>
The secondary overlap of the endo transition state are found at MO 16 and 22,which is not observed at the exo MOs.

{|
|[[File:Hgl_MO16_CHEMDRAW.png|thumb|150px|MO 16]]||[[File:HGl_Mo16_2nd_overlap.png|thumb|150px|MO 16]]||[[File:HGL_Mo22_2nd_overlap.png|thumb|150px|MO 22]]||[[File:HGL_MO_CHEMDRAW.png|thumb|150px|MO 22]]
|}

=== IRC ===
The IRC were calculated using the AM1/semi-empirical optimised structures at the same level.

{| class="wikitable" border="1"
|+ IRC
! Transition States !! Animation!! IRC energy diagram!!DOI
|-
| Endo || [[File: Hgl_ENDO_AM1-IRC.gif|200px]]||[[File:Hgl_Endo-irc_am1.png|400px]]||{{DOI|10042/to-59159}}
|-
| Exo || [[File:Hgl_ENXO_AM1-IRC.gif|200px]]|| [[File:Hgl_Exo_irc_am1.png|400px]]||{{DOI|10042/to-59158}}
|}

As seen in the animations, the transition states of both exo and endo adduct have been found.

= References =
<references/>

Hgl09: /* MO Analysis */

Module 3: Transition States and Reactivity

= Introduction =

Apart from studying the structures and bonding of molecules, computational chemistry is also a powerful tool used to study the transition states and reactivity of molecules. In this modules, the transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition are characterised using orbital-based methods. The reaction paths and barrier heights are calculated as well.

= The Cope Rearrangement =

The [3,3]-sigmatropic rearrangement undergoes via the following reaction scheme:

[[File: Hgl_Reaction_schemecope.png|300px]]

There are two possible transition structures, a ''chair'' and a ''boat''. The ''boat'' is known to have a higher energy than the ''chair''.<ref>O. Wiest, K.A. Black and K.N. Houk, ''J. Am. Chem. Soc.'', '''1994''', 116, 10336-10337 {{DOI|10.1021/ja00101a078}}</ref> In this experiment, such activation energies and enthalpies are calculated using Gaussian09W.

== Optimising the Reactants and Products ==

=== Optimisation of 1,5-hexadiene ===

The anti structure was optimized at the HF/3-21G level with %mem=250MB. The structure obtained after optimisation has a point group of C2. A gauche structure was created by adjusting the dihedral angles of the optimised anti structure, submitted with the same setting used for the anti one. The point group obtained is also C2. The summary of optimisation of both structures are shown below. It would be expected the anti structure has lower energy than that of the gauche one since there are less steric effect.

{|
|[[File: Hgl_Anti_opt.png|thumb|250px|optimisation of ''anti1'' linkage structure]]

|[[File: Hgl_250mb_Gauche_opt.png|thumb|250px|optimisation of ''gauche2'' linkage structure]]
|}

Referring to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1], it is found that the anti structure obtained is ''anti1'' while the gauche structure obtained is ''gauche2''.

{| border="3" style="margin-left: 3em;"
|+ Optimisation of 1,5-hexadiene of '''C2''' symmetry
|-
! scope="col" | Structures
! scope="col" | Total Enegy (a.u.)
! scope="col" | Energy (kJ/mol)
|-
! scope="row" | anti1
<jmol>
<jmolApplet>
<title>anti1</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Anti1_optsturcture.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69260
| -145389.3
|-
! scope="row" | gauche2
<jmol>
<jmolApplet>
<title>gauche2</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Gauche2_opt.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69167
| -145388.7
|}

The results do agree with the prediction. Since the four centre carbons on anti1 all have antiperiplanar confomations, it was predicted to be the one having the lowest energies. To test my hypothesis, several ''anti'' and ''gauche'' structures were tested and the results are all summarized in the Table 1.

{| class="wikitable" border="1"
|+ Table 1: Optimisation of different conformers of 1,5-hexadiene
! Conformers !! Total Energy(a.u)!! Point Group!! Relative Energy (kcal/mol)!! References
|-
| <jmolFile text=anti1>Hgl_Anti1_optsturcture.mol</jmolFile> || -231.69260 || C2 || 0.04 || {{DOI|10042/to-57902}}
|-
| <jmolFile text=anti2>Hgl hexadiene Anti2.mol</jmolFile> || -231.69254 || Ci || 0.08 || {{DOI|10042/to-58114}}
|-
| <jmolFile text=anti3>Hgl hexanedieneAnti3.mol</jmolFile> || -231.68907 || C2h || 2.25 || {{DOI|10042/to-57929}}
|-
| <jmolFile text=anti4>Hgl hexadiene Anti4.mol</jmolFile> || -231.69097 || C1 || 1.06 || {{DOI|10042/to-58343}}
|-
| <jmolFile text=gauche1>Hgl_Gauche1.mol</jmolFile> || -231.68772 || C2 || 3.10 || {{DOI|10042/to-57930}}
|-
| <jmolFile text=gauche2>Hgl_Gauche2_opt.mol</jmolFile> || -231.69167 || C2 || 0.62 || {{DOI|10042/to-57903}}
|-
| <jmolFile text=gauche3>Hgl_Gauche3.mol</jmolFile> || -231.69266 || C1 || 0.00 || {{DOI|10042/to-58234}}
|-
| <jmolFile text=gauche4>Hgl_Gauche4.mol</jmolFile> || -231.69153 || C2 || 0.71 || {{DOI|10042/to-58118}}
|-
| <jmolFile text=gauche5>Hgl_Gauche5.mol</jmolFile> || -231.68962 || C1 || 1.91 || {{DOI|10042/to-58543}}
|-
| <jmolFile text=gauche6>Hgl_Gauche6.mol</jmolFile> || -231.68916 || C1 || 2.20 || {{DOI|10042/to-58544}}
|}

Surprisingly, gauche3 turns out to be the one having the lowest energy and the predicted structure anti1 is the 2nd lowest energy among the tested structures. However, the difference between them is not significant. A further test was carried out using B3LYP/6-31G* levels. The results obtained do agree with the prediction. The results are shown in Table 2.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | Conformers
! scope="col" | Total Enegy (a.u.)
! scope="col" | Relative Energy (kcal/mol)
! scope="col" | Point Group
! scope="col" | DOI
|-
! scope="row" | anti1
| -234.61179
| 0.00
| C2
| {{DOI|10042/to-58564}}
|-
! scope="row" | gauche3
| -234.61133
| 0.29
| C2
| {{DOI|10042/to-58562}}
|}

After optimisation at higher levels, anti1 has the lowest energy than that of gauche3, which agrees with my prediction. However, the high stability of gauche3 is due to the stabilisation resulted from overlap of the C=C π orbital with the C-H σ orbital<ref>A. Spivey, Lec 1, {{DOI|http://www.ch.ic.ac.uk/spivey/teaching/org3stereoelectronics/lecture11112.pdf}}</ref>, dominant over the steric repulsion within the structure.

=== Ci anti2 conformer ===

==== Optimisation of Ci anti2 conformer ====

Ci anti2 of 1,5-hexadiene was also optimised at the B3LYP/6-31G*. The final structures are compared in Table 3. The structures are symmetrical and therefore only half of the bond lengths and dihedral angles are reported.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | [[File: Hgl_Anti2_labelled.png|anti2 Conformer]]
! scope="col" | Total Enegy (a.u.)
! scope="col" | Point Group
! scope="col" | Bond Length (Å)
! scope="col" | DOI
|-
! scope="row" | anti2 optimised at HF/3-21G
| -231.69254
| Ci
| C(14)=C(12) 1.32; C(12)-C(9) 1.51; C(9)-C(6)1.55; C(14)-H(15) 1.07; C(12)-H(13) 1.08; C(9)-H(10) 1.09
| {{DOI|10042/to-58114}}
|-
! scope="row" | anti2 optimised at B3LYP/6-31G*
| -234.61171
| Ci
|C(14)=C(12) 1.33; C(12)-C(9) 1.50; C(9)-C(6)1.55; C(14)-H(15) 1.09; C(12)-H(13) 1.09; C(9)-H(10) 1.10
|{{DOI|10042/to-58419}}
|}

The C=C double bonds become longer and the C-C bonds are shorted after optimisating at the higher DFT/6-31G*. The difference between the enegy is about 2.9 a.u. which is equivalent to 7614kJ/mol. The overall geometry roughly stays the same.

==== Frequency Analysis ====

A frequency calculation was submitted to SCAN using the optimised anti2 conformers obtained at B3LYP/6-31G*. All vibrational frequencies obtained are real and positive. In addition, another frequency calculation was carried at 0K by setting the temperature at 0.00001K and pressure at 1 atm. The results are shown below. It is found that at absolute zero temperature, all four sums are the same. The sum of electronic and zero-point energies of the one at 298.15K roughly agrees with the one obtained at 0K.

{| class="wikitable" border="1"
|+ Frequency Analysis of anti2 conformer
! !!Frequency analysis at 298.15K !! Frequency analysis at 0K
|-
| IR spectrum|| [[File:Hgl_Anti2_ir_298.15.png|300px]]|| [[File:Hgl_Anti2_ir_ok.png|300px]]
|-
| Sum of electronic and zero-point energies (E=Eelec+ZPE) (a.u.)|| -234.469204|| -234.468766
|-
| Sum of electronic and thermal energies (E=E+Evib+ Erot+Etrans) (a.u.)|| -234.461857|| -234.468766
|-
| Sum of electronic and thermal enthalpies (H=E+RT) (a.u.)|| -234.460913|| -234.468766
|-
| Sum of electronic and thermal free energies (G=H-TS) (a.u.)|| -234.50077|| -234.468766
|-
| DOI||{{DOI|10042/to-58427}}|| {{DOI|10042/to-58598}}
|}

== Optimizing the ''Chair'' and ''Boat'' Transition Structures ==

In this section, the ''chair'' and ''boat'' transition structure optimisations for the Cope rearrangement were set up by
#computing the force constants at the beginning of the calculation;
#using the redundant coordinate editor;
#using QST2.

IRC(Intrinisic Reaction Coordinate) of both structures were run and the activation energies for the rearrangement via both transition structures were obtained.

=== Chair Transition State ===
An <jmolFile text=allyl fragement>Hgl_Gauche2_opt.mol</jmolFile> was created using GaussView 5.0. It was optimised using the HF/3-21G level of theory. The chair transition state was created using two of such fragment, the distance between the terminal ends of the fragments was set to 2.2Å. The ''chair'' structure was then optimised by using the methoeds mentioned in the previous section.

* Chair(b): Optimisating by Computing the force constants at the beginning of the calculation
The created ''chair'' transition states was optimised to a '''TS(Berny)''' by calculating the force constants '''once''' with ''Opt=NoEigen'' at the additional keyword box and a frequency calculation was also included. The calculated structure is a C2h ''chair''. The terminal ends of the two fragments are 2.02Å apart. In the frequency analysis, an imaginary frequency is found at -818cm-1, which confirms the existence of the transition state. The animated vibration is shown below.

[[File: Hgl_Chair_ts_img_vib.gif|thumb|300px|imaginary vibration of the chair transition structure]]

* Chair(d): Optimisaing using the redundant coordinate editor
The tranistion structure was optimised again using the frozen coordinate methods. The distances between the terminal C ends were ''freezed'' to 2.2Å and was optimised to a minimum with ''Opt=ModRedundant'' included in the input file. The optimised structure (chair (c)) looks similar to the one obtained from the previous section. Since the terminal distance was freezed, the distance between them is still 2.2Å. A further optimisation was set up using '''Redundant Coord Editor'''. The Bond was set to ''Derivative'' and a transition state optimised was set up with calculation of the force constant set to '''Never'''. The obtained structure looks again the same as the ones obtained in the previous section, and the distance between the terminal C ends is also the same, 2.02Å.

{| class="wikitable" border="1"
|+ Optimisation of ''chair'' transition state
! Optimisation methods!! Optimisating by Computing the force constants at the beginning of the calculation!! Optimisaing using the redundant coordinate editor (freezed bond length)!!Optimisaing using the redundant coordinate editor (derivative bond length)
|-
| Energy (a.u.) || -231.61932|| -231.61519|| -231.61932
|-
| Terminal C ends distance(Å) || 2.02|| 2.20|| 2.02
|-
| Jmol || <jmolFile text=chair(b)>Hgl_Chair_opt_b.mol</jmolFile>|| <jmolFile text=chair(c)>Hgl_Chair_opt_c.mol</jmolFile>|| <jmolFile text=chair(d)>Hgl_Chair_opt_d.mol</jmolFile>
|-
| DOI || {{DOI|10042/to-58130}}|| {{DOI|10042/to-58129}}|| {{DOI|10042/to-58136}}
|}

=== Boat Transition State ===

The ''boat'' transition state was optimised using QST2 method. The reactant molecule used was anti2 conformer. Two molecules were set up in the same window and the two structures were oriented following the lab script. The atoms were labelled to have the atoms on the product all match the reactant molecule.

{|
|[[File: Hgl_Boat_scheme.png|400px]]
|[[File:Hgl_Boat_qst2_fail.png|400px]]
|}

The structure was then submitted to scan for transition state optimisation and a frequency calculation was also included. The script used was shown below:
---------------------------------------------------
# opt=(calcfc,qst2) freq hf/3-21g geom=connectivity
---------------------------------------------------
However, the optimisation failed as the sturcture obtained looks more like a dissociated ''chair'' transition state. A similar imaginary vibration to the chair structure is also found at -818cm-1, which further confirms the structure obtained is the chair transition state.
{|
![[File:HGL_Boat_qst2_FAIL_1.png|thumb|middle|200px|failed boat transition structure optimisation]]
![[File: Hgl_Boat_qst2.png|thumb|middle|400px|modified structure for boat optimisation]]
|}

The original input file was then modified to make it look as close to the boat transition state as possible. Both the reactant and product had the central C-C-C-C- dihedral angle set to 0o, with the inside C-C-C reduced to 100o.

{| class="wikitable" border="1"
|+ Optimisation of Boat transition state
! Summary !! [[File:Hgl_Boat_qst2_summary.png|300px]]
|-
| Terminal C ends distance || 2.14
|-
|Imiginary vibration at -840cm-1|| [[Image:Hgl_Boat_vib.gif|thumb|300px|click to start it]]
|-
| DOI || {{DOI|10042/to-58156}}
|}

=== Intrinsic Reaction Coordinate (IRC) Analysis ===

Intrinsic Reaction Coordinate(IRC) is a method providing information on the minimum energy path from the transition structure down to its local minimum on a potential energy surface. The IRC was calculated using the optimised transition structures from the previous sections. As the reaction coordinate is symmetrical, only forward direction was chose to be computed and the force constant was calculated once with number of points along the IRC set to 50.

It was found that the IRC terminated at step 21 but it hadn't reached a minimum. The final structure obtained looks more like the structure used for the boat tranistion state optimisation. The total energy is -231.687731a.u.
{| class="wikitable" border="1"
|+ IRC calculation
! Resulted conformer !! IRC Diagram!! RMS Gradient
|-
| [[File:Hgl_Chair_irc.gif|200px]]|| [[File:Hgl Chair irc energy.png|300px]]|| [[File:Hgl_Chair_irc_rms.png|300px]]
|}
{{DOI|10042/to-58735}}

Three different methods were then used to make the IRC reach a minimum geometry.

(i)''Take the last step of IRC and run a normal minimisation''

A normal optimisation to a minimum was set up using the final structure obtained from the previous IRC calculation. The calculation finished very fast. However, the structure obtained is the same as gauche2 with the same total energy, -231.69167 a.u and point group C2. This indicates the ''chair'' transition structure leads to the gauche2 conformer.

(ii)''Restart the IRC and set the no. of points along the IRC 100''

The same result was obtained as running the IRC with the no. of points along the IRC set to 50. Therefore, this method isn't much improvement either.

(iii)''Redo the IRC and compute the force constants at each step''

The force constant was set to '''always''' while the other settings were kept the same as the initial IRC calculation. The results obtained has the similar total energy as the one obtained using (i), -231.69166 a.u. This is again confirms that the ''chair'' transition state leads to gauche2 conformer. This method terminates at step 47.

{| class="wikitable" border="1"
|+ IRC calculation using different methods
! Methods !!(i) !! (ii) !! (iii)
|-
| Animation|| [[File:Hgl_Chair_irc_1.gif|200px]] || [[File:Hgl_Chair_irc_2.gif|200px]] || [[File:Hgl_Chair_irc_3.gif|200px]]
|-
| Total Energy (a.u) || -231.69167 || -231.68514 || -231.69166
|-
| IRC Total Energy Graph|| [[File:Hgl_Chair_irc_i_energy.png|300px]] || [[File: Hgl_Chair_irc_ii_energy.png|300px]] || [[File: Hgl_Chair_irc_iii_energy.png|300px]]
|-
| IRC RMS|| [[File:Hgl_Chair_irc_i_rms.png|300px]] || [[File:Hgl_Chair_irc_ii_rms.png|300px]] || [[File:Hgl_Chair_irc_iii_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58745}} || {{DOI|10042/to-58747}} || {{DOI|10042/to-58748}}
|}

In conclusion, it is found that method (iii) could be the best choice among the three as it only requires one IRC calculation which would have reached the minimum geometry. Therefore, the IRC calculation of the ''boat'' transition state was carried out using method(iii). The structure obtained at the final step is a gauche conformer of point group C1.

{| class="wikitable" border="1"
|+ IRC calculation of ''boat'' transition state
! Animation !! [[File:Hgl_Boat_irc.gif|200px]]
|-
| Total Energy (a.u.) || -231.68528
|-
| IRC Total Energy Graph || [[File: Hgl_Boat_irc_energy.png|300px]]
|-
| IRC RMS || [[File: Hgl_Boat_irc_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58238}}
|}

=== Activation Energies ===

Both ''chair'' and ''boat'' transition structures were optimised at B3LYP/6-31G* levle of theory using the HF/3-21G optimised structures. The activation energy is obtained by finding the difference between the reactants and transition states with the corresponding calculating methods. The methods used are listed below. Since the sum of electronic and zero-point energy at different temperatures roughly agrees, the sum was obtained from the 298.15K .log file.

{| class="wikitable" border="1"
|+ Optimisation of transition states
! Transition States!! Optimisation Methods !! Point Groups !! Electronic Energy (a.u)!! Sum of electronic and zero-point energies at 298.15K(a.u)!! Sum of electronic and thermal energies at 0K(a.u.)!! Terminal C ends distance (Å) !! Activation Energies at 298.15K(kcal/mol)!! Activation Energies at 0K(kcal/mol)!!DOI
|-
| Reactant (anti2) || HF/3-21G|| C2v ||-231.69254|| -231.52681|| -231.53907|| N/A|| N/A|| N/A || 0K {{DOI|10042/to-59019}};278.15K {{DOI|10042/to-59025}}
|-
| Reactant (anti2) || B31YP/6-31G*|| C2v ||-234.61171|| -234.46143|| -234.46877|| N/A|| N/A||N/A || 0K {{DOI|10042/to-58598}}; 278.15K {{DOI|10042/to-58556}}
|-
| chair || HF/3-21G || C2h || -231.61932|| -231.46132|| -231.46667|| 2.02 || 41.1|| 45.4|| 278.15K {{DOI|10042/to-58969}}
|-
| chair || B31YP/6-31G*|| C2h|| -234.55698|| -234.40901|| -234.41493|| 1.97 || 32.9|| 33.8|| 278.15K {{DOI|10042/to-58414}}
|-
| boat || HF/3-21G || C2v || -231.60280|| -231.44530|| -231.45093|| 2.14 || 51.1|| 46.5|| 278.15K {{DOI|10042/to-58972}}
|-
| boat || B31YP/6-31G*|| C2v || -234.54309||-234.39601||-234.40234|| 2.21|| 41.1|| 41.7|| 278.15K{{DOI|10042/to-59053}}
|}

As seen in the above table, the chair transition state has a lower activation energy than the boat one, which indicates chair transition state pathway would be more favoured in the Cope rearrangement. The experimental activation enegies are 33.5±0.5cal/mol via the chair transition state and 44.7±2.0kcal/mol.<ref> Mod3:phy https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3</ref> The computational results using DFT/6-31G* roughly agrees with it.

= Diels Alder Cycloaddition =

Diels Alder cycloaddition is a type of pericyclic reaction, occuring between a conjugated diene and a dienophile. An aromatic transition state of six delocalised π electrons is formed. <ref>J. Claden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, 2001, pp905-906 ISBN: 978-0-19-850346-0</ref> In this section, the transition states of two π4s+π2s reaction are calculated, starting with AM1/semi-empricial level.

== Diels Alder reaction between ethylene and butadiene ==

{|
|[[File: Hgl_Diels_alder_scheme_1.png|thumb|350px|Diels Alder reaction between ethylene and butadiene]]
|}

=== cis butadiene and ethylene MO symmetry determinations ===

The cis-butadiene was optimised at AM1 semi-empirical level, using Gaussian09W.

{| class="wikitable" border="1"
|+ Optimisation of cis-butadiene
! Molecules!!Total Energy (a.u) !! HOMO (a.u)!! LUMO (a.u)!!C=C Bond Lengths (Å)|| C-C Bond Length (Å)!!.log
|-
| Cis-butadiene|| 0.048797|| [[File:Hgl_Cis-butadiene_homo.png|thumb|250px| -0.34381(Symmetry=a)]]|| [[File: Hgl_Cis-butadiene_lumo.png|thumb|250px| 0.01707(Symmetry=s)]]|| 1.34||1.45||[[File:Hgl_CISBUTADIENE_OPT.LOG]]
|-
| Ethylene|| 0.02619|| [[File:Hgl_Ethylene_homo.png|thumb|250px| -0.38775(Symmetry=s)]]||[[File:Hgl_Ethylene_lumo.png|thumb|250px|0.05283(Symmetry=a)]]||1.33|| n/a||[[File:Hgl_ethylene_OPT.LOG]]
|}

It can be clearly seen the LUMOs and HOMOs are formed from p-orbital overlapping, forming π bonds. The HOMO of the cis-butadiene has the same symmetry as the LUMO of ethylene, both antisymmetrical whereas the LUMO of the cis-butadiene and HOMO of the ethylene are both symmetrical. Therefore, the the orbitals of the same symmetry can interact with each other and the reaction is allowed. Both the HOMO and LUMO of cis-butadiene have negative energies. Thus, the energies of new σ bond orbitals formed decreases relative to the ones of ethylene.<ref>Molecular Orbitals In Conjugated System, http://www.chem.ucsb.edu/~kalju/chem109C/DielsAlder.html</ref>

=== Transition state ===

The transition state was set up using the optimised cis-butadiene and ethylene structures. It was first guessed using the redundant coord editor method and was then optimised to a transition state (''TS Berny'') at AM1-semiexpirical level. The distance between the C atoms where the two newly formed σ bonds form was froze to 2.2Å to start the optimisation. A frequency calculation was also carried out.
{| class="wikitable" border="1"
|+ Optimisation of Transition States
! Methods!! Freeze Coordinate (2.2Å) !! Freeze Coordinate (Derivative) !! TS(Berny) opt at semi-emprical/AM1
|-
| Total Energies (a.u) || 0.10745|| 0.11166|| 0.11165
|-
| Point Groups || Cs|| Cs|| Cs
|-
| Partyly formed C-C Distance (Å) || 2.20|| 2.12|| 2.12
|-
| Diene C-C Bond Length (Å)|| 1.42|| 1.40||1.40
|-
| Diene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| Ethylene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| DOI || {{DOI|10042/to-59109}}|| {{DOI|10042/to-59116}}|| {{DOI|10042/to-59121}}
|}

At the transition state, the C=C bond of both reactants get longer as when the two new σ bonds are forming at these positions, electrons transferring from the π orbitals into the corresponding LUMO and HOMO as mentioned above. An imaginary vibration is found in the frequency analysis, which confirms the transition state has been found and π electrons transferred in a concerted stereospecific fashion.

{| class="wikitable" border="1"
|+ Imiaginary and the lowest positive Vibration
! wavelength (cm-1) !! Animation!! Description
|-
| -956|| [[File:Hgl_cyclehexene_ts_2,4vib.gif|250px]]|| Synchronous movement of both fragments towards each other
|-
| 142|| [[File:Hgl_Lowest_positive_cyclohexene_vib.gif|250px]]|| Synchronous rocking of both fragments
|}

{| class="wikitable" border="1"
|+ Tranistion MO Analysis
! MOs!! HOMO !! LUMO
|-
| MO Images || [[File:HGL_CYCLOHEXENE_TS_HOMO.png|thumb|250px|symmetry=a]]|| [[File:HGL_CYCLOHEXENE_TS_LUMO.png|thumb|250px|symmetry=s]]
|-
| MO energies (a.u) || -0.32394|| 0.02315
|-
| Symmetries || Antisymmetric || Symmetrical
|}

The HOMO and LUMO of the transition states agrees with the prediction mentioned at the reactants MO sections. The electrons are transferred from the π orbitals which is the HOMO of one fragment into the π* which is the LUMO of the other fragment, forming the new σ orbitals, having the same symmetry as the orbitals generate them.

=== IRC ===
The IRC calculated at AM1/semi-emprical level further confirms the completion of finding the transition state. The final step structure has a symmetry of Cs.

{|
|[[File: Hgl_Irc_cyclohexene_ts.gif|thumb|250px|animation of IRC]]
|[[File: Hgl_Irc_cyclohexene.png|thumb|400px| IRC energy graph]]
|}

{{DOI|10042/to-58843}}

== Regioselectivity of the Diels Alder Reaction between Cyclohexa-1,3-diene and maleic anhydride==
There are two possible products in the Diels Alder reaction between cyclic diene and dienophile, ''endo'' and ''exo'' adducts. In this section, the transition states formed between cyclohexa-1,3-diene and maleic anhydride were tested to study the kinetics of the reaction.
{|
|[[File:Hgl_DIELS_ALDER_SCHEME_2.png|thumb|350px|Diels Alder reaction between cyclohexa-1,3-diene and maleic anhydride]]
|}

=== MO Analysis ===
Again, both cyclohexa-1,3-diene and maleic anhydride structures were optimised at AM1 semi-empirical level before starting any transition state calculation.
{| class="wikitable" border="1"
|+ Optimisation
! Molecules!! Total Energy (a.u.) !! HOMO(a.u.)!! LUMO(a.u)!!.log
|-
| Cyclohexa-1,3-diene || 0.02771|| [[File:Hgl_1,3cyclohexadiene_homo.png|thumb|250px|-0.32194(Symmetry=a)]]|| [[File:Hgl_1,3cyclohexadiene_lumo.png|thumb|250px|0.01680(Symmetry=s)]]|| {{DOI|10042/to-59077}}
|-
| Maleic Anhydride || -0.12182|| [[File:Hgl_Maleic_anhydride_homo.png|thumb|250px|-0.44187(Symmetry=s)]]||[[File:Hgl_Maleic_anhydride_lumo.png|thumb|250px|-0.05949(Symmetry=a)]]|| [[File:Hgl_MALEIC_ANHYDRIDE.LOG]]
|}

Both HOMO and LUMO of maleic anhydride have negative energies, resulting from the presence of more electronegative O atoms. The lower energy of LUMO enables better orbital overlapping with the HOMO of diene. <ref>''Zeolite Characterization and Catalysis: a Tutorial (google ebook, pphttp://books.google.co.uk/books?id=UobhZh216WkC&pg=PA309&lpg=PA309&dq=homo+maleic+anhydride+diels+alder&source=bl&ots=pbb1sW5nSv&sig=eEpKj8gcNSJvVJhwZA4EKIGJBVM&hl=en&sa=X&ei=YEhrT6OMEMix0AWosaDBBg&ved=0CFQQ6AEwCTgK#v=onepage&q=homo%20maleic%20anhydride%20diels%20alder&f=false</ref>

=== Transition State ===
The transition states were set up by using the optimised maleic anhydride and cyclohexa-1,3-diene. Both structures were optimised using redundant coord editor method. The structures obtained were then optimised further using AM1/semi-emprical to TS(Berny) and frequency analysis were included as well. The partyly forming σ bonds were set to 2.2Å at the beginning of the freeze coordinate optimisation.The optimisation results are tabulated.

{| class="wikitable" border="1"
|+ Transition States Optimisation
! !!Endo Adduct !! Endo Adduct!! Exo Adduct!! Exo Adduct
|-
|Methods|| Redundant Coor Editor|| TS(Berny)|| Redundant Coor Editor|| TS(Berny)
|-
| Final structures|| [[File:Hgl_Endo_freeze.png|200px]] || [[File:Hgl_Endo_tsberny.png|200px]]||[[File:Hgl_Exo_freeze.png|200px]]|| [[File:Hgl_Exo_tsberny.png|200px]]
|-
| Total Energies (a.u)|| -0.06945|| -0.05150|| -0.06959|| -0.05042
|-
| Imaginary Vibration (cm-1)|| n/a|| -806|| n/a|| -812
|-
| Partly Forming σ C-C Bond Length (Å)|| 2.00|| 2.16 || 2.00|| 2.17
|-
| Diene C=C Bond (Å)|| 1.50|| 1.39|| 1.45|| 1.39
|-
| Diene C-C Bond (Å)|| 1.53|| 1.40|| 1.36|| 1.40
|-
| Anhydride C=C Bond (Å) || 1.47|| 1.41|| 1.47|| 1.41
|-
|DOI||{{DOI|10042/to-58705}}||{{DOI|10042/to-58708}}|| {{DOI|10042/to-58714}}|| {{DOI|10042/to-58719}}
|}

All the structures obtained have the same point group: Cs. By studying the imaginary vibrations of both, it is confirmed that the transition structures have been found.

Both endo and exo products were optimised at AM1/semi-emprical level. By studying into the log file, the following data can be obtained.<ref>http://www.chem.ucsb.edu/~kalju/chem111/public/qm_ts_hcn_hnc.html</ref>

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Total Energy (a.u)!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!!Sum of electronic and thermal free energies(a.u.)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!!ΔG(kcal/mol)!! DOI
|-
| Maleic Anhydride|| -0.05819|| -0.06335|| -0.05819|| -0.09250||||||||||||{{DOI|10042/to-59151}}
|-
| Cyclo-1,3-diene|| 0.02771|| 0.15250|| 0.15773|| 0.12449||||||||||||{{DOI|10042/to-59152}}
|-
| Reactants Total|| -0.03048|| 0.08915|| 0.09954|| 0.03199||||||||||||n/a
|-
| Endo TS|| -0.05150|| 0.13349|| 0.14368|| 0.09735|| 27.8|| 27.7||||||||{{DOI|10042/to-58708}}
|-
| Endo Product|| -0.16017|| 0.03146|| 0.04046|| -0.00316|| || ||-36.2|| -37.1|| -22.1||{{DOI|10042/to-59146}}
|-
| Exo TS ||-0.05042|| 0.13488|| 0.14488|| 0.09912|| 29.7|| 28.5|| ||||||{{DOI|10042/to-58719}}
|-
| Exo Product|| -0.15991|| 0.03170|| 0.04068|| -0.00288|| || || -36.1|| -37.0|| -62.9||{{DOI|10042/to-59147}}
|}

As found in the Cope rearrangement, the results obtained using DFT/6-31g* method are more accurately. i.e. the optimisation was then carried out at DFT/6-31G* level.

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Electronic Energy!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!! Sum of electronic and thermal free energies (a.u)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!! ΔG(a.u)!! DOI
|-
| Maleic Anhydride|| -379.28954|| -379.23366|| -379.22847|| -379.26273||||||||||||{{DOI|10042/to-59155}}
|-
| Cyclo-1,3-diene|| -233.41891|| -233.29610|| -233.29092|| -233.32370||||||||||||{{DOI|10042/to-59154}}
|-
| Reactants Total|| -612.70845|| -612.52976|| -612.51939|| -612.58643||||||||||||n/a
|-
| Endo TS|| -612.68340|| -612.50214|| -612.49179|| -612.53833|| 17.3|| 17.3||||||||{{DOI|10042/to-58758}}
|-
| Endo Product|| -612.75829|| -612.57207|| -612.56261|| -612.60718|| || || -26.5|| -27.1|| -13.0||{{DOI|10042/to-59157}}
|-
| Exo TS || -612.67931|| -612.49801|| -612.48766|| -612.53426|| 19.3|| 19.9|||| ||||{{DOI|10042/to-58757}}
|-
| Exo Product|| -612.75579|| -612.56938|| -612.55998|| -612.60428|| || || -24.9|| -25.5|| -11.2||{{DOI|10042/to-59156}}
|}

The results obtained using both methods exhibit the same trend: the endo transition state has the lower activation energy, which means it is the endo product is the kinetic product. i.e., the exo product is thermodynamic product.

=== Bonding interaction and Secondary Orbital Overlap ===

{| class="wikitable" border="1"
|+ MO Analysis
! MOs !! HOMO-1!! HOMO!! LUMO!! LUMO+1!! Energies
|-
| Exo Adduct || [[File:Hgl_Exo_homo-1.png|150px]]|| [[File:Hgl-Exo_homo.png|150px]]|| [[File:Hgl_Exo_lumo.png|150px]]||[[File:Hgl_Exo_lumo+1.png|150px]]||[[File:Hgl_Exo_energy.png|150px]]
|-
| Endo Adduct || [[File:Hgl_Endo_homo-1.png|150px]]|| [[File:Hgl_Endo_homo.png|150px]]||[[File:Hgl_Endo_lumo.png|150px]]||[[File:Hgl_Endo_lumo+1.png|150px]]||[[File:Hgl_Endo_energy.png|150px]]
|}

It can be clearly seen that the endo adduct MOs have lower energy than those of exo adduct.

The endo transition has the lower energy as a result of secondary orbital overlap.<ref>T.L. Gilchrist, R.C. Storr, ''Organic Reactions and Orbital Symmetry'', pp119 ISBN:9780521293365</ref>
The secondary overlap of the endo transition state are found at MO 16 and 22,which is not observed at the exo MOs.

{|
|[[File:Hgl_MO16_CHEMDRAW.png|thumb|150px|MO 16]]||[[File:HGl_Mo16_2nd_overlap.png|thumb|150px|MO 16]]||[[File:HGL_Mo22_2nd_overlap.png|thumb|150px|MO 22]]||[[File:HGL_MO_CHEMDRAW.png|thumb|150px|MO 22]]
|}

=== IRC ===
The IRC were calculated using the AM1/semi-empirical optimised structures at the same level.

{| class="wikitable" border="1"
|+ IRC
! Transition States !! Animation!! IRC energy diagram!!DOI
|-
| Endo || [[File: Hgl_ENDO_AM1-IRC.gif|300px]]||[[File:Hgl_Endo-irc_am1.png|450px]]||{{DOI|10042/to-59159}}
|-
| Exo || [[File:Hgl_ENXO_AM1-IRC.gif|300px]]|| [[File:Hgl_Exo_irc_am1.png|450px]]||{{DOI|10042/to-59158}}
|}

= References =
<references/>

Rep:Mod:hgl0903

2012-03-22T16:22:28Z

Hgl09: /* MO Analysis */

Module 3: Transition States and Reactivity

= Introduction =

Apart from studying the structures and bonding of molecules, computational chemistry is also a powerful tool used to study the transition states and reactivity of molecules. In this modules, the transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition are characterised using orbital-based methods. The reaction paths and barrier heights are calculated as well.

= The Cope Rearrangement =

The [3,3]-sigmatropic rearrangement undergoes via the following reaction scheme:

[[File: Hgl_Reaction_schemecope.png|300px]]

There are two possible transition structures, a ''chair'' and a ''boat''. The ''boat'' is known to have a higher energy than the ''chair''.<ref>O. Wiest, K.A. Black and K.N. Houk, ''J. Am. Chem. Soc.'', '''1994''', 116, 10336-10337 {{DOI|10.1021/ja00101a078}}</ref> In this experiment, such activation energies and enthalpies are calculated using Gaussian09W.

== Optimising the Reactants and Products ==

=== Optimisation of 1,5-hexadiene ===

The anti structure was optimized at the HF/3-21G level with %mem=250MB. The structure obtained after optimisation has a point group of C2. A gauche structure was created by adjusting the dihedral angles of the optimised anti structure, submitted with the same setting used for the anti one. The point group obtained is also C2. The summary of optimisation of both structures are shown below. It would be expected the anti structure has lower energy than that of the gauche one since there are less steric effect.

{|
|[[File: Hgl_Anti_opt.png|thumb|250px|optimisation of ''anti1'' linkage structure]]

|[[File: Hgl_250mb_Gauche_opt.png|thumb|250px|optimisation of ''gauche2'' linkage structure]]
|}

Referring to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1], it is found that the anti structure obtained is ''anti1'' while the gauche structure obtained is ''gauche2''.

{| border="3" style="margin-left: 3em;"
|+ Optimisation of 1,5-hexadiene of '''C2''' symmetry
|-
! scope="col" | Structures
! scope="col" | Total Enegy (a.u.)
! scope="col" | Energy (kJ/mol)
|-
! scope="row" | anti1
<jmol>
<jmolApplet>
<title>anti1</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Anti1_optsturcture.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69260
| -145389.3
|-
! scope="row" | gauche2
<jmol>
<jmolApplet>
<title>gauche2</title><color>white</color><size>150</size>
<uploadedFileContents>Hgl_Gauche2_opt.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| -231.69167
| -145388.7
|}

The results do agree with the prediction. Since the four centre carbons on anti1 all have antiperiplanar confomations, it was predicted to be the one having the lowest energies. To test my hypothesis, several ''anti'' and ''gauche'' structures were tested and the results are all summarized in the Table 1.

{| class="wikitable" border="1"
|+ Table 1: Optimisation of different conformers of 1,5-hexadiene
! Conformers !! Total Energy(a.u)!! Point Group!! Relative Energy (kcal/mol)!! References
|-
| <jmolFile text=anti1>Hgl_Anti1_optsturcture.mol</jmolFile> || -231.69260 || C2 || 0.04 || {{DOI|10042/to-57902}}
|-
| <jmolFile text=anti2>Hgl hexadiene Anti2.mol</jmolFile> || -231.69254 || Ci || 0.08 || {{DOI|10042/to-58114}}
|-
| <jmolFile text=anti3>Hgl hexanedieneAnti3.mol</jmolFile> || -231.68907 || C2h || 2.25 || {{DOI|10042/to-57929}}
|-
| <jmolFile text=anti4>Hgl hexadiene Anti4.mol</jmolFile> || -231.69097 || C1 || 1.06 || {{DOI|10042/to-58343}}
|-
| <jmolFile text=gauche1>Hgl_Gauche1.mol</jmolFile> || -231.68772 || C2 || 3.10 || {{DOI|10042/to-57930}}
|-
| <jmolFile text=gauche2>Hgl_Gauche2_opt.mol</jmolFile> || -231.69167 || C2 || 0.62 || {{DOI|10042/to-57903}}
|-
| <jmolFile text=gauche3>Hgl_Gauche3.mol</jmolFile> || -231.69266 || C1 || 0.00 || {{DOI|10042/to-58234}}
|-
| <jmolFile text=gauche4>Hgl_Gauche4.mol</jmolFile> || -231.69153 || C2 || 0.71 || {{DOI|10042/to-58118}}
|-
| <jmolFile text=gauche5>Hgl_Gauche5.mol</jmolFile> || -231.68962 || C1 || 1.91 || {{DOI|10042/to-58543}}
|-
| <jmolFile text=gauche6>Hgl_Gauche6.mol</jmolFile> || -231.68916 || C1 || 2.20 || {{DOI|10042/to-58544}}
|}

Surprisingly, gauche3 turns out to be the one having the lowest energy and the predicted structure anti1 is the 2nd lowest energy among the tested structures. However, the difference between them is not significant. A further test was carried out using B3LYP/6-31G* levels. The results obtained do agree with the prediction. The results are shown in Table 2.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | Conformers
! scope="col" | Total Enegy (a.u.)
! scope="col" | Relative Energy (kcal/mol)
! scope="col" | Point Group
! scope="col" | DOI
|-
! scope="row" | anti1
| -234.61179
| 0.00
| C2
| {{DOI|10042/to-58564}}
|-
! scope="row" | gauche3
| -234.61133
| 0.29
| C2
| {{DOI|10042/to-58562}}
|}

After optimisation at higher levels, anti1 has the lowest energy than that of gauche3, which agrees with my prediction. However, the high stability of gauche3 is due to the stabilisation resulted from overlap of the C=C π orbital with the C-H σ orbital<ref>A. Spivey, Lec 1, {{DOI|http://www.ch.ic.ac.uk/spivey/teaching/org3stereoelectronics/lecture11112.pdf}}</ref>, dominant over the steric repulsion within the structure.

=== Ci anti2 conformer ===

==== Optimisation of Ci anti2 conformer ====

Ci anti2 of 1,5-hexadiene was also optimised at the B3LYP/6-31G*. The final structures are compared in Table 3. The structures are symmetrical and therefore only half of the bond lengths and dihedral angles are reported.

{| class="wikitable" border="1"
|+ Table 2: Optimisation at B3LYP/6-31G*
|-
! scope="col" | [[File: Hgl_Anti2_labelled.png|anti2 Conformer]]
! scope="col" | Total Enegy (a.u.)
! scope="col" | Point Group
! scope="col" | Bond Length (Å)
! scope="col" | DOI
|-
! scope="row" | anti2 optimised at HF/3-21G
| -231.69254
| Ci
| C(14)=C(12) 1.32; C(12)-C(9) 1.51; C(9)-C(6)1.55; C(14)-H(15) 1.07; C(12)-H(13) 1.08; C(9)-H(10) 1.09
| {{DOI|10042/to-58114}}
|-
! scope="row" | anti2 optimised at B3LYP/6-31G*
| -234.61171
| Ci
|C(14)=C(12) 1.33; C(12)-C(9) 1.50; C(9)-C(6)1.55; C(14)-H(15) 1.09; C(12)-H(13) 1.09; C(9)-H(10) 1.10
|{{DOI|10042/to-58419}}
|}

The C=C double bonds become longer and the C-C bonds are shorted after optimisating at the higher DFT/6-31G*. The difference between the enegy is about 2.9 a.u. which is equivalent to 7614kJ/mol. The overall geometry roughly stays the same.

==== Frequency Analysis ====

A frequency calculation was submitted to SCAN using the optimised anti2 conformers obtained at B3LYP/6-31G*. All vibrational frequencies obtained are real and positive. In addition, another frequency calculation was carried at 0K by setting the temperature at 0.00001K and pressure at 1 atm. The results are shown below. It is found that at absolute zero temperature, all four sums are the same. The sum of electronic and zero-point energies of the one at 298.15K roughly agrees with the one obtained at 0K.

{| class="wikitable" border="1"
|+ Frequency Analysis of anti2 conformer
! !!Frequency analysis at 298.15K !! Frequency analysis at 0K
|-
| IR spectrum|| [[File:Hgl_Anti2_ir_298.15.png|300px]]|| [[File:Hgl_Anti2_ir_ok.png|300px]]
|-
| Sum of electronic and zero-point energies (E=Eelec+ZPE) (a.u.)|| -234.469204|| -234.468766
|-
| Sum of electronic and thermal energies (E=E+Evib+ Erot+Etrans) (a.u.)|| -234.461857|| -234.468766
|-
| Sum of electronic and thermal enthalpies (H=E+RT) (a.u.)|| -234.460913|| -234.468766
|-
| Sum of electronic and thermal free energies (G=H-TS) (a.u.)|| -234.50077|| -234.468766
|-
| DOI||{{DOI|10042/to-58427}}|| {{DOI|10042/to-58598}}
|}

== Optimizing the ''Chair'' and ''Boat'' Transition Structures ==

In this section, the ''chair'' and ''boat'' transition structure optimisations for the Cope rearrangement were set up by
#computing the force constants at the beginning of the calculation;
#using the redundant coordinate editor;
#using QST2.

IRC(Intrinisic Reaction Coordinate) of both structures were run and the activation energies for the rearrangement via both transition structures were obtained.

=== Chair Transition State ===
An <jmolFile text=allyl fragement>Hgl_Gauche2_opt.mol</jmolFile> was created using GaussView 5.0. It was optimised using the HF/3-21G level of theory. The chair transition state was created using two of such fragment, the distance between the terminal ends of the fragments was set to 2.2Å. The ''chair'' structure was then optimised by using the methoeds mentioned in the previous section.

* Chair(b): Optimisating by Computing the force constants at the beginning of the calculation
The created ''chair'' transition states was optimised to a '''TS(Berny)''' by calculating the force constants '''once''' with ''Opt=NoEigen'' at the additional keyword box and a frequency calculation was also included. The calculated structure is a C2h ''chair''. The terminal ends of the two fragments are 2.02Å apart. In the frequency analysis, an imaginary frequency is found at -818cm-1, which confirms the existence of the transition state. The animated vibration is shown below.

[[File: Hgl_Chair_ts_img_vib.gif|thumb|300px|imaginary vibration of the chair transition structure]]

* Chair(d): Optimisaing using the redundant coordinate editor
The tranistion structure was optimised again using the frozen coordinate methods. The distances between the terminal C ends were ''freezed'' to 2.2Å and was optimised to a minimum with ''Opt=ModRedundant'' included in the input file. The optimised structure (chair (c)) looks similar to the one obtained from the previous section. Since the terminal distance was freezed, the distance between them is still 2.2Å. A further optimisation was set up using '''Redundant Coord Editor'''. The Bond was set to ''Derivative'' and a transition state optimised was set up with calculation of the force constant set to '''Never'''. The obtained structure looks again the same as the ones obtained in the previous section, and the distance between the terminal C ends is also the same, 2.02Å.

{| class="wikitable" border="1"
|+ Optimisation of ''chair'' transition state
! Optimisation methods!! Optimisating by Computing the force constants at the beginning of the calculation!! Optimisaing using the redundant coordinate editor (freezed bond length)!!Optimisaing using the redundant coordinate editor (derivative bond length)
|-
| Energy (a.u.) || -231.61932|| -231.61519|| -231.61932
|-
| Terminal C ends distance(Å) || 2.02|| 2.20|| 2.02
|-
| Jmol || <jmolFile text=chair(b)>Hgl_Chair_opt_b.mol</jmolFile>|| <jmolFile text=chair(c)>Hgl_Chair_opt_c.mol</jmolFile>|| <jmolFile text=chair(d)>Hgl_Chair_opt_d.mol</jmolFile>
|-
| DOI || {{DOI|10042/to-58130}}|| {{DOI|10042/to-58129}}|| {{DOI|10042/to-58136}}
|}

=== Boat Transition State ===

The ''boat'' transition state was optimised using QST2 method. The reactant molecule used was anti2 conformer. Two molecules were set up in the same window and the two structures were oriented following the lab script. The atoms were labelled to have the atoms on the product all match the reactant molecule.

{|
|[[File: Hgl_Boat_scheme.png|400px]]
|[[File:Hgl_Boat_qst2_fail.png|400px]]
|}

The structure was then submitted to scan for transition state optimisation and a frequency calculation was also included. The script used was shown below:
---------------------------------------------------
# opt=(calcfc,qst2) freq hf/3-21g geom=connectivity
---------------------------------------------------
However, the optimisation failed as the sturcture obtained looks more like a dissociated ''chair'' transition state. A similar imaginary vibration to the chair structure is also found at -818cm-1, which further confirms the structure obtained is the chair transition state.
{|
![[File:HGL_Boat_qst2_FAIL_1.png|thumb|middle|200px|failed boat transition structure optimisation]]
![[File: Hgl_Boat_qst2.png|thumb|middle|400px|modified structure for boat optimisation]]
|}

The original input file was then modified to make it look as close to the boat transition state as possible. Both the reactant and product had the central C-C-C-C- dihedral angle set to 0o, with the inside C-C-C reduced to 100o.

{| class="wikitable" border="1"
|+ Optimisation of Boat transition state
! Summary !! [[File:Hgl_Boat_qst2_summary.png|300px]]
|-
| Terminal C ends distance || 2.14
|-
|Imiginary vibration at -840cm-1|| [[Image:Hgl_Boat_vib.gif|thumb|300px|click to start it]]
|-
| DOI || {{DOI|10042/to-58156}}
|}

=== Intrinsic Reaction Coordinate (IRC) Analysis ===

Intrinsic Reaction Coordinate(IRC) is a method providing information on the minimum energy path from the transition structure down to its local minimum on a potential energy surface. The IRC was calculated using the optimised transition structures from the previous sections. As the reaction coordinate is symmetrical, only forward direction was chose to be computed and the force constant was calculated once with number of points along the IRC set to 50.

It was found that the IRC terminated at step 21 but it hadn't reached a minimum. The final structure obtained looks more like the structure used for the boat tranistion state optimisation. The total energy is -231.687731a.u.
{| class="wikitable" border="1"
|+ IRC calculation
! Resulted conformer !! IRC Diagram!! RMS Gradient
|-
| [[File:Hgl_Chair_irc.gif|200px]]|| [[File:Hgl Chair irc energy.png|300px]]|| [[File:Hgl_Chair_irc_rms.png|300px]]
|}
{{DOI|10042/to-58735}}

Three different methods were then used to make the IRC reach a minimum geometry.

(i)''Take the last step of IRC and run a normal minimisation''

A normal optimisation to a minimum was set up using the final structure obtained from the previous IRC calculation. The calculation finished very fast. However, the structure obtained is the same as gauche2 with the same total energy, -231.69167 a.u and point group C2. This indicates the ''chair'' transition structure leads to the gauche2 conformer.

(ii)''Restart the IRC and set the no. of points along the IRC 100''

The same result was obtained as running the IRC with the no. of points along the IRC set to 50. Therefore, this method isn't much improvement either.

(iii)''Redo the IRC and compute the force constants at each step''

The force constant was set to '''always''' while the other settings were kept the same as the initial IRC calculation. The results obtained has the similar total energy as the one obtained using (i), -231.69166 a.u. This is again confirms that the ''chair'' transition state leads to gauche2 conformer. This method terminates at step 47.

{| class="wikitable" border="1"
|+ IRC calculation using different methods
! Methods !!(i) !! (ii) !! (iii)
|-
| Animation|| [[File:Hgl_Chair_irc_1.gif|200px]] || [[File:Hgl_Chair_irc_2.gif|200px]] || [[File:Hgl_Chair_irc_3.gif|200px]]
|-
| Total Energy (a.u) || -231.69167 || -231.68514 || -231.69166
|-
| IRC Total Energy Graph|| [[File:Hgl_Chair_irc_i_energy.png|300px]] || [[File: Hgl_Chair_irc_ii_energy.png|300px]] || [[File: Hgl_Chair_irc_iii_energy.png|300px]]
|-
| IRC RMS|| [[File:Hgl_Chair_irc_i_rms.png|300px]] || [[File:Hgl_Chair_irc_ii_rms.png|300px]] || [[File:Hgl_Chair_irc_iii_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58745}} || {{DOI|10042/to-58747}} || {{DOI|10042/to-58748}}
|}

In conclusion, it is found that method (iii) could be the best choice among the three as it only requires one IRC calculation which would have reached the minimum geometry. Therefore, the IRC calculation of the ''boat'' transition state was carried out using method(iii). The structure obtained at the final step is a gauche conformer of point group C1.

{| class="wikitable" border="1"
|+ IRC calculation of ''boat'' transition state
! Animation !! [[File:Hgl_Boat_irc.gif|200px]]
|-
| Total Energy (a.u.) || -231.68528
|-
| IRC Total Energy Graph || [[File: Hgl_Boat_irc_energy.png|300px]]
|-
| IRC RMS || [[File: Hgl_Boat_irc_rms.png|300px]]
|-
| DOI || {{DOI|10042/to-58238}}
|}

=== Activation Energies ===

Both ''chair'' and ''boat'' transition structures were optimised at B3LYP/6-31G* levle of theory using the HF/3-21G optimised structures. The activation energy is obtained by finding the difference between the reactants and transition states with the corresponding calculating methods. The methods used are listed below. Since the sum of electronic and zero-point energy at different temperatures roughly agrees, the sum was obtained from the 298.15K .log file.

{| class="wikitable" border="1"
|+ Optimisation of transition states
! Transition States!! Optimisation Methods !! Point Groups !! Electronic Energy (a.u)!! Sum of electronic and zero-point energies at 298.15K(a.u)!! Sum of electronic and thermal energies at 0K(a.u.)!! Terminal C ends distance (Å) !! Activation Energies at 298.15K(kcal/mol)!! Activation Energies at 0K(kcal/mol)!!DOI
|-
| Reactant (anti2) || HF/3-21G|| C2v ||-231.69254|| -231.52681|| -231.53907|| N/A|| N/A|| N/A || 0K {{DOI|10042/to-59019}};278.15K {{DOI|10042/to-59025}}
|-
| Reactant (anti2) || B31YP/6-31G*|| C2v ||-234.61171|| -234.46143|| -234.46877|| N/A|| N/A||N/A || 0K {{DOI|10042/to-58598}}; 278.15K {{DOI|10042/to-58556}}
|-
| chair || HF/3-21G || C2h || -231.61932|| -231.46132|| -231.46667|| 2.02 || 41.1|| 45.4|| 278.15K {{DOI|10042/to-58969}}
|-
| chair || B31YP/6-31G*|| C2h|| -234.55698|| -234.40901|| -234.41493|| 1.97 || 32.9|| 33.8|| 278.15K {{DOI|10042/to-58414}}
|-
| boat || HF/3-21G || C2v || -231.60280|| -231.44530|| -231.45093|| 2.14 || 51.1|| 46.5|| 278.15K {{DOI|10042/to-58972}}
|-
| boat || B31YP/6-31G*|| C2v || -234.54309||-234.39601||-234.40234|| 2.21|| 41.1|| 41.7|| 278.15K{{DOI|10042/to-59053}}
|}

As seen in the above table, the chair transition state has a lower activation energy than the boat one, which indicates chair transition state pathway would be more favoured in the Cope rearrangement. The experimental activation enegies are 33.5±0.5cal/mol via the chair transition state and 44.7±2.0kcal/mol.<ref> Mod3:phy https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3</ref> The computational results using DFT/6-31G* roughly agrees with it.

= Diels Alder Cycloaddition =

Diels Alder cycloaddition is a type of pericyclic reaction, occuring between a conjugated diene and a dienophile. An aromatic transition state of six delocalised π electrons is formed. <ref>J. Claden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, 2001, pp905-906 ISBN: 978-0-19-850346-0</ref> In this section, the transition states of two π4s+π2s reaction are calculated, starting with AM1/semi-empricial level.

== Diels Alder reaction between ethylene and butadiene ==

{|
|[[File: Hgl_Diels_alder_scheme_1.png|thumb|350px|Diels Alder reaction between ethylene and butadiene]]
|}

=== cis butadiene and ethylene MO symmetry determinations ===

The cis-butadiene was optimised at AM1 semi-empirical level, using Gaussian09W.

{| class="wikitable" border="1"
|+ Optimisation of cis-butadiene
! Molecules!!Total Energy (a.u) !! HOMO (a.u)!! LUMO (a.u)!!C=C Bond Lengths (Å)|| C-C Bond Length (Å)!!.log
|-
| Cis-butadiene|| 0.048797|| [[File:Hgl_Cis-butadiene_homo.png|thumb|250px| -0.34381(Symmetry=a)]]|| [[File: Hgl_Cis-butadiene_lumo.png|thumb|250px| 0.01707(Symmetry=s)]]|| 1.34||1.45||[[File:Hgl_CISBUTADIENE_OPT.LOG]]
|-
| Ethylene|| 0.02619|| [[File:Hgl_Ethylene_homo.png|thumb|250px| -0.38775(Symmetry=s)]]||[[File:Hgl_Ethylene_lumo.png|thumb|250px|0.05283(Symmetry=a)]]||1.33|| n/a||[[File:Hgl_ethylene_OPT.LOG]]
|}

It can be clearly seen the LUMOs and HOMOs are formed from p-orbital overlapping, forming π bonds. The HOMO of the cis-butadiene has the same symmetry as the LUMO of ethylene, both antisymmetrical whereas the LUMO of the cis-butadiene and HOMO of the ethylene are both symmetrical. Therefore, the the orbitals of the same symmetry can interact with each other and the reaction is allowed. Both the HOMO and LUMO of cis-butadiene have negative energies. Thus, the energies of new σ bond orbitals formed decreases relative to the ones of ethylene.<ref>Molecular Orbitals In Conjugated System, http://www.chem.ucsb.edu/~kalju/chem109C/DielsAlder.html</ref>

=== Transition state ===

The transition state was set up using the optimised cis-butadiene and ethylene structures. It was first guessed using the redundant coord editor method and was then optimised to a transition state (''TS Berny'') at AM1-semiexpirical level. The distance between the C atoms where the two newly formed σ bonds form was froze to 2.2Å to start the optimisation. A frequency calculation was also carried out.
{| class="wikitable" border="1"
|+ Optimisation of Transition States
! Methods!! Freeze Coordinate (2.2Å) !! Freeze Coordinate (Derivative) !! TS(Berny) opt at semi-emprical/AM1
|-
| Total Energies (a.u) || 0.10745|| 0.11166|| 0.11165
|-
| Point Groups || Cs|| Cs|| Cs
|-
| Partyly formed C-C Distance (Å) || 2.20|| 2.12|| 2.12
|-
| Diene C-C Bond Length (Å)|| 1.42|| 1.40||1.40
|-
| Diene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| Ethylene C=C Bond Length (Å)|| 1.36|| 1.38|| 1.38
|-
| DOI || {{DOI|10042/to-59109}}|| {{DOI|10042/to-59116}}|| {{DOI|10042/to-59121}}
|}

At the transition state, the C=C bond of both reactants get longer as when the two new σ bonds are forming at these positions, electrons transferring from the π orbitals into the corresponding LUMO and HOMO as mentioned above. An imaginary vibration is found in the frequency analysis, which confirms the transition state has been found and π electrons transferred in a concerted stereospecific fashion.

{| class="wikitable" border="1"
|+ Imiaginary and the lowest positive Vibration
! wavelength (cm-1) !! Animation!! Description
|-
| -956|| [[File:Hgl_cyclehexene_ts_2,4vib.gif|250px]]|| Synchronous movement of both fragments towards each other
|-
| 142|| [[File:Hgl_Lowest_positive_cyclohexene_vib.gif|250px]]|| Synchronous rocking of both fragments
|}

{| class="wikitable" border="1"
|+ Tranistion MO Analysis
! MOs!! HOMO !! LUMO
|-
| MO Images || [[File:HGL_CYCLOHEXENE_TS_HOMO.png|thumb|250px|symmetry=a]]|| [[File:HGL_CYCLOHEXENE_TS_LUMO.png|thumb|250px|symmetry=s]]
|-
| MO energies (a.u) || -0.32394|| 0.02315
|-
| Symmetries || Antisymmetric || Symmetrical
|}

The HOMO and LUMO of the transition states agrees with the prediction mentioned at the reactants MO sections. The electrons are transferred from the π orbitals which is the HOMO of one fragment into the π* which is the LUMO of the other fragment, forming the new σ orbitals, having the same symmetry as the orbitals generate them.

=== IRC ===
The IRC calculated at AM1/semi-emprical level further confirms the completion of finding the transition state. The final step structure has a symmetry of Cs.

{|
|[[File: Hgl_Irc_cyclohexene_ts.gif|thumb|250px|animation of IRC]]
|[[File: Hgl_Irc_cyclohexene.png|thumb|400px| IRC energy graph]]
|}

{{DOI|10042/to-58843}}

== Regioselectivity of the Diels Alder Reaction between Cyclohexa-1,3-diene and maleic anhydride==
There are two possible products in the Diels Alder reaction between cyclic diene and dienophile, ''endo'' and ''exo'' adducts. In this section, the transition states formed between cyclohexa-1,3-diene and maleic anhydride were tested to study the kinetics of the reaction.
{|
|[[File:Hgl_DIELS_ALDER_SCHEME_2.png|thumb|350px|Diels Alder reaction between cyclohexa-1,3-diene and maleic anhydride]]
|}

=== MO Analysis ===
Again, both cyclohexa-1,3-diene and maleic anhydride structures were optimised at AM1 semi-empirical level before starting any transition state calculation.
{| class="wikitable" border="1"
|+ Optimisation
! Molecules!! Total Energy (a.u.) !! HOMO(a.u.)!! LUMO(a.u)!!.log
|-
| Cyclohexa-1,3-diene || 0.02771|| [[File:Hgl_1,3cyclohexadiene_homo.png|thumb|250px|-0.32194(Symmetry=a)]]|| [[File:Hgl_1,3cyclohexadiene_lumo.png|thumb|250px|0.01680(Symmetry=s)]]|| {{DOI|10042/to-59077}}
|-
| Maleic Anhydride || -0.12182|| [[File:Hgl_Maleic_anhydride_homo.png|thumb|250px|-0.44187(Symmetry=s)]]||[[File:Hgl_Maleic_anhydride_lumo.png|thumb|250px|-0.05949(Symmetry=a)]]|| [[File:Hgl_MALEIC_ANHYDRIDE.LOG]]
|}

Both HOMO and LUMO of maleic anhydride have negative energies, resulting from the presence of more electronegative O atoms. The lower energy of LUMO enables better orbital overlapping with the HOMO of diene. <ref>''Zeolite Characterization and Catalysis: a Tutorial (google ebook, pp{{DOI|http://books.google.co.uk/books?id=UobhZh216WkC&pg=PA309&lpg=PA309&dq=homo+maleic+anhydride+diels+alder&source=bl&ots=pbb1sW5nSv&sig=eEpKj8gcNSJvVJhwZA4EKIGJBVM&hl=en&sa=X&ei=YEhrT6OMEMix0AWosaDBBg&ved=0CFQQ6AEwCTgK#v=onepage&q=homo%20maleic%20anhydride%20diels%20alder&f=false}}</ref>

=== Transition State ===
The transition states were set up by using the optimised maleic anhydride and cyclohexa-1,3-diene. Both structures were optimised using redundant coord editor method. The structures obtained were then optimised further using AM1/semi-emprical to TS(Berny) and frequency analysis were included as well. The partyly forming σ bonds were set to 2.2Å at the beginning of the freeze coordinate optimisation.The optimisation results are tabulated.

{| class="wikitable" border="1"
|+ Transition States Optimisation
! !!Endo Adduct !! Endo Adduct!! Exo Adduct!! Exo Adduct
|-
|Methods|| Redundant Coor Editor|| TS(Berny)|| Redundant Coor Editor|| TS(Berny)
|-
| Final structures|| [[File:Hgl_Endo_freeze.png|200px]] || [[File:Hgl_Endo_tsberny.png|200px]]||[[File:Hgl_Exo_freeze.png|200px]]|| [[File:Hgl_Exo_tsberny.png|200px]]
|-
| Total Energies (a.u)|| -0.06945|| -0.05150|| -0.06959|| -0.05042
|-
| Imaginary Vibration (cm-1)|| n/a|| -806|| n/a|| -812
|-
| Partly Forming σ C-C Bond Length (Å)|| 2.00|| 2.16 || 2.00|| 2.17
|-
| Diene C=C Bond (Å)|| 1.50|| 1.39|| 1.45|| 1.39
|-
| Diene C-C Bond (Å)|| 1.53|| 1.40|| 1.36|| 1.40
|-
| Anhydride C=C Bond (Å) || 1.47|| 1.41|| 1.47|| 1.41
|-
|DOI||{{DOI|10042/to-58705}}||{{DOI|10042/to-58708}}|| {{DOI|10042/to-58714}}|| {{DOI|10042/to-58719}}
|}

All the structures obtained have the same point group: Cs. By studying the imaginary vibrations of both, it is confirmed that the transition structures have been found.

Both endo and exo products were optimised at AM1/semi-emprical level. By studying into the log file, the following data can be obtained.<ref>http://www.chem.ucsb.edu/~kalju/chem111/public/qm_ts_hcn_hnc.html</ref>

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Total Energy (a.u)!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!!Sum of electronic and thermal free energies(a.u.)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!!ΔG(kcal/mol)!! DOI
|-
| Maleic Anhydride|| -0.05819|| -0.06335|| -0.05819|| -0.09250||||||||||||{{DOI|10042/to-59151}}
|-
| Cyclo-1,3-diene|| 0.02771|| 0.15250|| 0.15773|| 0.12449||||||||||||{{DOI|10042/to-59152}}
|-
| Reactants Total|| -0.03048|| 0.08915|| 0.09954|| 0.03199||||||||||||n/a
|-
| Endo TS|| -0.05150|| 0.13349|| 0.14368|| 0.09735|| 27.8|| 27.7||||||||{{DOI|10042/to-58708}}
|-
| Endo Product|| -0.16017|| 0.03146|| 0.04046|| -0.00316|| || ||-36.2|| -37.1|| -22.1||{{DOI|10042/to-59146}}
|-
| Exo TS ||-0.05042|| 0.13488|| 0.14488|| 0.09912|| 29.7|| 28.5|| ||||||{{DOI|10042/to-58719}}
|-
| Exo Product|| -0.15991|| 0.03170|| 0.04068|| -0.00288|| || || -36.1|| -37.0|| -62.9||{{DOI|10042/to-59147}}
|}

As found in the Cope rearrangement, the results obtained using DFT/6-31g* method are more accurately. i.e. the optimisation was then carried out at DFT/6-31G* level.

{| class="wikitable" border="1"
|+ Summary of Energies
! !!Electronic Energy!! Sum of electronic and zero-point energies at 0K!! Sum of electronic and thermal energies at 298.15K!! Sum of electronic and thermal free energies (a.u)!! ΔEa at 0K(kcal/mol)!!ΔEa at 298.15K(kcal)!! ΔH at 0K(kcal/mol)!! ΔH at 298.15K(kcal/mol)!! ΔG(a.u)!! DOI
|-
| Maleic Anhydride|| -379.28954|| -379.23366|| -379.22847|| -379.26273||||||||||||{{DOI|10042/to-59155}}
|-
| Cyclo-1,3-diene|| -233.41891|| -233.29610|| -233.29092|| -233.32370||||||||||||{{DOI|10042/to-59154}}
|-
| Reactants Total|| -612.70845|| -612.52976|| -612.51939|| -612.58643||||||||||||n/a
|-
| Endo TS|| -612.68340|| -612.50214|| -612.49179|| -612.53833|| 17.3|| 17.3||||||||{{DOI|10042/to-58758}}
|-
| Endo Product|| -612.75829|| -612.57207|| -612.56261|| -612.60718|| || || -26.5|| -27.1|| -13.0||{{DOI|10042/to-59157}}
|-
| Exo TS || -612.67931|| -612.49801|| -612.48766|| -612.53426|| 19.3|| 19.9|||| ||||{{DOI|10042/to-58757}}
|-
| Exo Product|| -612.75579|| -612.56938|| -612.55998|| -612.60428|| || || -24.9|| -25.5|| -11.2||{{DOI|10042/to-59156}}
|}

The results obtained using both methods exhibit the same trend: the endo transition state has the lower activation energy, which means it is the endo product is the kinetic product. i.e., the exo product is thermodynamic product.

=== Bonding interaction and Secondary Orbital Overlap ===

{| class="wikitable" border="1"
|+ MO Analysis
! MOs !! HOMO-1!! HOMO!! LUMO!! LUMO+1!! Energies
|-
| Exo Adduct || [[File:Hgl_Exo_homo-1.png|150px]]|| [[File:Hgl-Exo_homo.png|150px]]|| [[File:Hgl_Exo_lumo.png|150px]]||[[File:Hgl_Exo_lumo+1.png|150px]]||[[File:Hgl_Exo_energy.png|150px]]
|-
| Endo Adduct || [[File:Hgl_Endo_homo-1.png|150px]]|| [[File:Hgl_Endo_homo.png|150px]]||[[File:Hgl_Endo_lumo.png|150px]]||[[File:Hgl_Endo_lumo+1.png|150px]]||[[File:Hgl_Endo_energy.png|150px]]
|}

It can be clearly seen that the endo adduct MOs have lower energy than those of exo adduct.

The endo transition has the lower energy as a result of secondary orbital overlap.<ref>T.L. Gilchrist, R.C. Storr, ''Organic Reactions and Orbital Symmetry'', pp119 ISBN:9780521293365</ref>
The secondary overlap of the endo transition state are found at MO 16 and 22,which is not observed at the exo MOs.

{|
|[[File:Hgl_MO16_CHEMDRAW.png|thumb|150px|MO 16]]||[[File:HGl_Mo16_2nd_overlap.png|thumb|150px|MO 16]]||[[File:HGL_Mo22_2nd_overlap.png|thumb|150px|MO 22]]||[[File:HGL_MO_CHEMDRAW.png|thumb|150px|MO 22]]
|}

=== IRC ===
The IRC were calculated using the AM1/semi-empirical optimised structures at the same level.

{| class="wikitable" border="1"
|+ IRC
! Transition States !! Animation!! IRC energy diagram!!DOI
|-
| Endo || [[File: Hgl_ENDO_AM1-IRC.gif|300px]]||[[File:Hgl_Endo-irc_am1.png|450px]]||{{DOI|10042/to-59159}}
|-
| Exo || [[File:Hgl_ENXO_AM1-IRC.gif|300px]]|| [[File:Hgl_Exo_irc_am1.png|450px]]||{{DOI|10042/to-59158}}
|}

= References =
<references/>