ChemWiki - User contributions [en]

Rep:Mod:andyr2911

2015-03-27T03:40:13Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|350px|Optimised allyl fragment]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==

The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:38:49Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px|Optimised allyl fragment]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==

The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:38:29Z

Ar2312: /* Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px|Optimised allyl fragment]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==

The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:36:56Z

Ar2312: /* Diels-Alder Reaction */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px|Optimised allyl fragment]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==

The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

File:Diels alder54.png

2015-03-27T03:35:42Z

Ar2312:

Rep:Mod:andyr2911

2015-03-27T03:29:04Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px|Optimised allyl fragment]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:28:47Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px|Optimised ally fragment]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:27:19Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|center|300px]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:25:09Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|300px]]
<title>QTS 2</title><color>darkgreen</color>
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:24:27Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|300px]]
|}
The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:23:31Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|300px]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:21:48Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif|thumb|200px]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:16:35Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{| align="center" border="4"
|-
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:15:50Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{align="center"|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:12:12Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry further stabilising the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:10:44Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The imaginary frequency for the Endo and Exo transition States were -445,67cm1 and -447,87cm1. The endo product is selectively preferred over the exo product and this is supported by experimental procedures. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>. The endo product is the kinetic product due to the same symmetry of the reactants and this further stabilises the transition state.

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:05:13Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:04:56Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:04:40Z

Ar2312: /* Endo and Exo Transition States */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>
{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:03:38Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>

{| align="center" border="4"
|-
!Calculation Information !!Exo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:02:36Z

Ar2312: /* Exo Transition State */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Endo and Exo Transition States===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:01:58Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T03:01:32Z

Ar2312: /* Exo Transition State */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

<div style="float: left; width:100%; padding-bottom:20px; padding-top:10px;">
<gallery mode="packed-hover" heights="250">
File:EXOTRANSV.gif| Exo TS
File:HOMO4exo.jpg| Homo Exo TS
File:Endo TS movie.gif| Endo TS
File:Homoendots.gif| Homo Endo TS
</gallery>
<div style="padding-left:10px;"> '
</div>

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|200px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:56:35Z

Ar2312: /* Exo Transition State */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|} [[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|200px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|200px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:54:50Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|200px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:54:30Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|300px|thumb|left| Endo TS]]
[[File:Homoendots.gif|300px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:54:09Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|200px|thumb|left| Endo TS]]
[[File:Homoendots.gif|100px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:53:50Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|20px|thumb|left| Endo TS]]
[[File:Homoendots.gif|10px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:53:22Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|200px|thumb|left| Endo TS]]
[[File:Homoendots.gif|100px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:52:53Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|200px|thumb|left| Endo TS]]
[[File:Homoendots.gif|150px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:52:39Z

Ar2312: /* Endo transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|150px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:52:23Z

Ar2312: /* Exo Transition State */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|300px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|300px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:49:59Z

Ar2312: /* Opitimising and Locating the boat transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>QTS 2</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:48:53Z

Ar2312: /* Opitimising and Locating the boat transition state */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:47:03Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

{| align="center" border="0"
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]
|}

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:46:34Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>anti2 3-21G</title><color>darkgreen</color>
<size>300</size><script>rotate z 90; spin on;select ;measure 1 4;measure 4 6;measure 6 9; measure 9 12; measure 12 14; measure 1 4 6; measure 4 6 9; measure 6 9 12; measure 9 12 14;</script>
<uploadedFileContents>ALLY_FRAGMENT_OPT+FRE_MOVIE.gif</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:45:27Z

Ar2312: /* Optimisation of the Chair Transition State using the Frozen Coordinate Method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===

[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:42:29Z

Ar2312: /* Optimising the "Chair" and "Boat" Transition Structures */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgreen</color>
<size>200</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:42:01Z

Ar2312: /* Optimising the "Chair" and "Boat" Transition Structures */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>darkgrey</color>
<size>300</size>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:39:51Z

Ar2312: /* Optimising the "Chair" and "Boat" Transition Structures */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.
<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

{| align="center" border="0"
|| <jmol>
<jmolApplet>
<title>Allyl fragment optimised</title><color>#CCFFCC</color>
<size>300</size><script>rotate z 90; spin on;select ;measure 1 4;measure 4 6;measure 6 9; measure 9 12; measure 12 14; measure 1 4 6; measure 4 6 9; measure 6 9 12; measure 9 12 14;</script>
<uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:36:54Z

Ar2312: /* Optimising the "Chair" and "Boat" Transition Structures */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.
<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:36:38Z

Ar2312:

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.
<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:34:52Z

Ar2312: /* Optimising the "Chair" and "Boat" Transition Structures */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:32:40Z

Ar2312: /* Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:29:58Z

Ar2312: /* Intrinsic Reaction Coordinate method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data was retrieved:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

Rep:Mod:andyr2911

2015-03-27T02:29:42Z

Ar2312: /* Intrinsic Reaction Coordinate method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data was retrieved:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]
[[File:Graph34.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

File:Graph34.png

2015-03-27T02:29:18Z

Ar2312:

Rep:Mod:andyr2911

2015-03-27T02:25:19Z

Ar2312: /* Intrinsic Reaction Coordinate method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data was retrieved:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]
[[File:Anim56.gif|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>

File:Anim56.gif

2015-03-27T02:23:32Z

Ar2312:

Rep:Mod:andyr2911

2015-03-27T02:20:17Z

Ar2312: /* Intrinsic Reaction Coordinate method */

==The Cope Rearrangement==

The [3,3]-sigmatropic shift of 1,5-hexadiene was studied and the objective was to locate the low-energy minima and the transition structure on this compound, in order to determine the preferred mechanism.

There has been great interest in investigating the study of the mechanism. The mechanism (concerted,stepwise or dissociative) has been long debated. However, it has been widely accepted that the reaction proceeds in a concerted mechanism for the rearrangement. The reaction proceeds via the "boat" and "chair transition states structure. The B3LYP/6-31G* level of theory has been proven to be exceptional in giving activation energies and enthalpies which is concordant with the experiment determined values. This is a concise report on the location of the transition structures and low energy minima on the 1,5-hexadiene's potential energy surface. These results show the preferred transition structure for the mechanism for the Cope-rearrangement.

===Optimisation of an "anti" and "gauche" linkage 1,5-hexadiene===

{| align="center" border="4"
|-
!Calculation Information !!Anti 2!! Gauche 5
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-231.69253528 ||-231.68961573
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001891 || 0.00001489
|-
| '''Point Group'''||C1||C2
|}

Using GaussView, 1,5-hexadiene was drawn with an "anti" linkage, approximately an anti-periplanar conformation. The structure was cleaned using the clean function and was optimised at the HF/3-21G level of theory. This was symmetrised and anti conformer was obtained with C1 symmetry and an electronic energy of -231.693 which is concord with the literature value. This was found to be the anti 2 conformer. The above method was applied in the same fashion to a "gauche" conformation of 1,5-hexadiene.The point group was identified to be C2 and the electronic energy was -231.690. This was confirmed to be the gauche 5 conformer.

The anti conformer generated was predicted to have a lower energy due to less steric hindrance. Despite the anti conformers being generally lower than the gauche conformers, Gauche 3 has the lowest energy conformer. This arises due to the attractive interaction between an ethenyl proton and the pi orbital <ref>D. R. Lide Jr., "A survey of carbon-carbon bond lengths", Tetrahedron, 1962,17, 125</ref>.
The Ci anti 2 conformation of 1,5-hexadiene was optimised at HF/3-21G level of theory and its final energy was compared to B3LYP/6-21G* level of theory. This differences are observed in the table:

{| align="center" border="4"
|-
!Calculation Information !!Anti 2 HF/3-21G !! Anti 2 B3LYP
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-231.69253538 ||-234.55970458
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001893 ||0.00004327
|-
| '''Point Group'''||Ci||Ci
|}

The molecular structures have not changed and this was observed by looking at the bond lengths and angles which were similar with respect to one another. The electronic energy for the B3LYP/6-31G* level of theory was higher than the HF/3-21G. The higher level of theory is more accurate because it includes polarisation and the nature of the core electrons is improved. Therefore it is concluded that 6-31G* is more accurate than 3-21G. <ref>[[https://www.wavefun.com/support/sp_compfaq/Basis_Set_FAQ.html]]</ref>

Frequency calculation was examined on the anti 2 conformer for the optimised B3LYP/6-31G* structure. It was observed that the vibration frequencies were all positive and this suggests that the conformer has a local minimum electronic energy. The IR spectrum was plotted:

{| align="center" border="0"
||[[File:ANTI2SPECTRA.gif|IR Spectrum of the anti-2 conformer]]
|}

The thermochemistry data was retrieved:

{| align="center" border="4"
|-
!Sum of electronic and zero-point Energies (a.u)!!-233.269204
|-
| Sum of electronic and thermal Energies (a.u)||-233.261657
|-
| Sum of electronic and thermal Free Energies (a.u)|| -233.427768
|}

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

An allyl fragment CH2CHCH2 was drawn on Gaussview and optimised using HF/3-21G level theory.

{| align="center" border="4"
|-
!Calculation Information !!Allyl fragment HF/3-21G !! Chair TS HF/3-21g!!Boat TS QST2
|-
| '''Calculation type''' || FOPT||FOPT||FOPT
|-
| '''Calculation Method''' || RHF||RHF||RHF
|-
| '''Basis Set''' || 3-21G||3-21G||3-21G
|-
| '''Total Energy (a.u)'''||-115.59490537||-231.4794963||-231.61932213
|-
| '''RMS Gradient Norm (a.u.) '''||0.00005281 ||0.01935506||0.00003967
|-
| '''Dipole Moment (Debye)'''|| 0.0698||0.1039||0
|-
| '''Point Group'''||C2V||C1||C2H
|}

<jmol><jmolApplet><title>allyl fragment optimised</title><color>darkslategray</color><size>250</size><uploadedFileContents>Allyl fragment optimised.mol</uploadedFileContents></jmolApplet></jmol>

The optimised allyl fragment was copied twice into a new window and were orientated so that they look similar to the chair transition state. The terminal ends of the alkene were altered to be 2.2A apart. A Gaussian optimisation was set to TS(Berny) and the force constant calculation was changed to one. "Opt=NoEigen" was added to stop the calculation from crashing when more than one imaginary frequency is detected. The imaginary frequency of magniture was calculated to be -817.92cm-1 which is similar to the literature value of -818cm-1.

===Optimisation of the Chair Transition State using the Frozen Coordinate Method===
[[File:ALLY_FRAGMENT_OPT+FRE_MOVIE.gif]]

The Chair Transition State was frozen using the Redundant Coordination Editor and the bond lengths between the terminal allyl carbons was set to 2.2A. The optimisation was performed in the same way as before, with an additional input "Opt=ModRedundant". The resulted in a similar transition structure from before but with fixed bond lengths of approximately 2.2A.

===Opitimising and Locating the boat transition state===

The Ci anti 2 1,5-hexadiene reactant was numbered manually such that it mirrored the product. The boat transition state was located and optimised using the QST2 method instead of TS(Berny). This method generates the transition state by linearly interpolating between the reactants and the products.

<jmol><jmolApplet><title>Boat Conformation</title><color>darkslategray</color><size>250</size><uploadedFileContents>QST 2 BOAT.mol</uploadedFileContents></jmolApplet></jmol>

The imaginary frequency was found to be -839.83 cm-1, indicating that this was a transition state structure.

===Intrinsic Reaction Coordinate method===
This method allows to follow the minimum energy path from a transition structure down through the local minimum on a potential energy surface. This is achieved by taking small geometry steps at the steepest point in the PES. The reagent and the product are symmetrical thereby IRC was calculated in only the forward reaction. The boat transition state required around 50 number of points to reach the local minimum as its structure was predicted. The calculation itself was large in comparison to the previous optimisation. The transition state was not achieved on completion therefore optimisation under HF/3-21G level of theory was calculated because it is faster. Due to time constraint, the force constant could not be calculated at every step.

The local minimum was achieved before the estimated 50 number of points had completed leading to calculation to terminate. The graphs were plotted by selecting the IRC path. This shows that the minima was reached and both the 'RMS gradient norm' and the 'Total energy along IRC curve' have constant values. The 4th and 5th point were the steepest points.

[[File:Ircgraphic3.png|center|600px]]

===Activation energies of both transition structures===

The activation energies for both transition structures were calculated using B3LYP/6-21G* level of theory. The frequency was calculated once it was optimised.

{| align="center" border="4"
|-
!Calculation Information !!Chair TS!! Chair TS/6-31G*!!Boat TS 3-21G || Boat TS B3LYP/6-31G*
|-
| '''Calculation type''' || FOPT||FOPT||FOPT||FTS
|-
| '''Calculation Method''' || RHF||RHF||RHF||RB3LYP
|-
| '''Basis Set''' || 3-21G||6-31G*||3-21G||6-31G*
|-
| '''Total Energy (a.u)'''||-115.62304009||-231.52632247||-231.43132213||-234.32104499
|-
| '''RMS Gradient Norm (a.u.) '''||0.00002734 ||0.00000743||0.00003967||0.00003460
|-
| '''Dipole Moment (Debye)'''|| 0.0151||0||0||0.1432
|-
| '''Point Group'''||C1||C1||C2h||C2h
|-
|}

As previously discussed when changing the level of theory, the geometric are similar relative to each other but differ in their electronic energies. This is due to the accuracy of the B3LYP/6-31G* level of theory.

{| align="center" border="4"
! !!Chair TS!!Boat TS!!Anti-2 conformer
|-
|Sum of electronic and zero-point Energies (a.u)||-233.358204||-233.34231||-234.35121
|-
|Sum of electronic and thermal Energies (a.u)||-233.358107||-233.34031||-233.358116
|-
|Sum of electronic and thermal Free Energies (a.u)|| -233.410778||-233.33170||-233.41082
|}

The activation energy was calculated between the difference between the anti 2 conformer electronic energy and the transition state electronic energy. The electronic energies value were computed at 0K. Gaussian automatically corrects to 298.15 K. Herein, 0.1k was used successfully.

{| align="center" border="4"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||33.556 ||42.562
|-
|Activation energy 298.15 K (kcal/mol)||31.105||41.822
|-
|}

The chair transition state is preferred to the boat transition state due to the kinetic effects. Therefore thermodynamic conditions will favour the reaction to proceed via the chair transition state.

==Diels-Alder Reaction==
The Diels-Alder reaction is [4n+2] cycloaddition reaction. This involves the formation of new sigma bonds between a diene and a dienophile yielding a cyclohexane product. It is widely accepted that this reaction is a concerted pericyclic reaction. Diels-Alder reactions are stereospecific, it can proceed via two transition states the endo and exo. According to the Frontier Molecular Orbital theory, it is suggested that the stronger the orbital interaction between the dienophile's LUMO and the diene's HOMO, the greater the rate of reaction. However steric play a pivotal role and must be taken into account.

This study shows the transition states for the Diels-Alder reaction between ethylene and cis-butadiene and 1,3-cyclohexadiene and maleic anhydride. Using GaussView, cis butadiene was built and optimised. It was first symmetrised with AM1 semi-empirical MO method to edge towards the transition state. Optimisation using B3LYP/6-31G* level of theory was performed as shown in the table:

{| align="center" border="4"
|-
!Calculation Information !!AM1 Cis-Butadiene!!B3LYP/6-31G* Cis-Butadiene
|-
| '''Calculation type''' || FOPT||FOPT
|-
| '''Calculation Method''' || RAM 1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy (a.u)'''||-||-155.95382679
|-
| '''RMS Gradient Norm (a.u.) '''||0.00001745||0.00002505
|-
| '''Dipole Moment (Debye)'''||0.0414|| 0.0940
|-
| '''Point Group'''||C2V||C2V
|}

The same procedure was performed on ethene and the HOMO/LUMO molecular orbitals were observed in Gaussview.

{| align="center" border="4" color="#CCFFCC"
|-
!Molecular Orbital !!Image!!Symmetry
|-
| '''Cis Butadiene LUMO''' ||[[File:Arlumo.jpg|150px]]||'''Symmetric'''
|-
| '''Cis Butadiene HOMO''' ||[[File:Homo.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene LUMO''' ||[[File:Lumoethene1.jpg|150px]]||'''Anti-Symmetric'''
|-
| '''Ethene HOMO''' ||[[File:homoethene1.jpg|150px]]||'''Symmetric'''
|-
|}

===Computation of the transition state===
The transition state structure has an envelope structure and to obtain this geometry was to guess and optimise using the AM1 semi-empirical MO level of theory and then the commonly used B3LYP/6-31G.<ref>J. Braz. Chem. Soc. vol.12 no.5 São Paulo Sept./Oct. 2001</ref>.The calculations proceeded without any errors using the guessed structure. A frequency calculation step was performed, obtaining an imaginary frequency which verifies that this was a transition state structure.The reported values for the average sp3 C-C and sp2 C-C bond length are 1.53A and 1.33A respectively. However the transition state bond length lies in between these values indicating that the carbon atoms has a bond order magnitude between sp2 and sp3 hybridisation. The carbon van der Waals radius is 1.70A. The distance between the terminal carbons is less than twice the VDW radii indicating bonding interaction at the termini.

{| align="center" border="3" color="#CCFFCC"
|-
!Level of Theory!!Image
|-
| '''Semi-empirical AM1''' ||[[File:Tsam1.jpg|150px]]|
|-
| '''DFT B3LYP/6-31G''' ||[[File:Homo.jpg|150px]]|
|-
|}

===Regioselectivity of Diels-Alder===
The reaction between maleic anhydride and 1,3-cyclohexadiene gives both endo and expo products. The same methodology previously used was used again to optimise.

{| align="center" border="4"
|-
!Calculation Information !!Maleic Anhydride!! 1,3-cyclohexadiene
|-
| '''Calculation type''' || OPT+FREQ||OPT+FREQ
|-
| '''Calculation Method''' || RB3LYP||RB3LYP
|-
| '''Basis Set''' || 6-31G||6-31G
|-
| '''Total Energy (a.u)'''||-379.29272204 ||-233.4279251
|-
| '''RMS Gradient Norm (a.u.) '''||0.00003352 ||0.000031937
|-
| '''Dipole Moment (Debye)'''||4.0692 ||0.5686
|-
| '''Point Group'''||C2V||C2V
|-
|}

{| align="center" border="4"
|-
!Molecular Orbital!!Symmetry with respect to the plane of symmetry
|-
| '''Maleic Anhydride LUMO''' ||Symmetric
|-
| '''Maleic Anhydride HOMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene LUMO''' ||Anti-Symmetric
|-
| '''1,3-cyclohexadiene HOMO''' ||Symmetric
|-
|}

===Exo Transition State===

The optimisation was performed in the same manner as previously and it was faster.
{| align="center" border="4"
|-
!Calculation Information !!Endo Transition State Semi-empirical AM1!! Followed by DFT
|-
| '''Calculation type''' || FOTP||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.15990939||-612.68339679 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.00001728|| 0.00001270
|-
| '''Dipole Moment (Debye)'''|| 5.2575|| 6.1144
|-
|}

[[File:EXOTRANSV.gif|250px|thumb|left| Exo TS]]
[[File:HOMO4exo.jpg|150px|thumb|right| Homo Exo TS]]

===Endo transition state===

{| align="center" border="4"
|-
!Calculation Information !!endo TS semi-empirical/AM1!! Followed by DFT
|-
| '''Calculation type''' || FOPT||FREQ
|-
| '''Calculation Method''' || RAM1||RB3LYP
|-
| '''Basis Set''' || ZDO||6-31G*
|-
| '''Total Energy'''||-0.21387277||-613.78337132 a.u.
|-
| '''RMS Gradient Norm (a.u.)'''||0.000015929|| 0.01292432
|-
| '''Dipole Moment (Debye)'''|| 5.5057|| 6.1673
|-
|}

[[File:Endo TS movie.gif|250px|thumb|left| Endo TS]]
[[File:Homoendots.gif|250px|thumb|right|Homo Endo TS]]

The imaginary frequency for the endo and exo transition structure were respectively. It was observed that the endo product was the kinetic product due to the lower activation energy. This can be further explained by the secondary orbital overlap in the transition states. The new pie bond interacts with the orbitails of the carbonyl function group due to the same symmetry.

{|border="1"
! !!Chair TS!!Boat TS
|-
|Activation energy 0 K (kcal/mol)||18.331 ||20.224
|-
|Activation energy 298.15 K (kcal/mol)||18.405||20.224
|-
|}

The endo product is selectively preferred over the exo product and this is supported by experimental. <ref>Ben L. Feringa , Johannes C. De Jong ''J. Org. Chem.''; 1998 53 (5), pp 1125–112.</ref>

==Conclusions==

The transition states were successful and it was concluded that the chair transition state is lower in energy than the boat transition state.

For Diels-Alder cycloaddition reaction, the cis-butadiene and ethylene reaction was analysed and it was concluded through MO the symmetry conditions required for a Diels-Alder cycloaddition. The endo product was favored for the reaction between maleic anhydride and 1,3-cyclohexadiene due to the low activation energy barrier and the secondary orbital effect of the endo transition state.

==References==
<references>
{{reflist}}
</references>