ChemWiki - User contributions [en]

Rep:Mod:mod3 jb

2012-02-18T16:20:55Z

Jgb09: /* The TS */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Hexadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 hexadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

===Butadiene===

====Optimisation====

Butadiene was optimised using the AM1 semi-empirical method<ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>:

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene - Symmetric, B2''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene - Asymmetric, A2''']]

Cis Butadiene has C<sub>2V</sub> symmetry and its HOMO is asymmetric with respect to its principle plane of symmetry and was chosen over trans because it gives a better orbital overlap.

The below picture shows the plane of symmetry present in the molecular orbitals:

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

===The envelope===

The transition state structure resembles an envelope with ethene approaching butadiene from above.

To optimise the structure the freeze bond method was applied.
The first structure obatined by freezing the coordinates is here: {{DOI|10042/to-12420}}

The final structure of the transition state is here: {{DOI|10042/to-12421}}

The HOMO and LUMO of the transition structure are outlined below:

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

As you can see from the diagram, the HOMO consists of two σ-bonds formed through the overlap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene. The LUMO is formed of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene. This confirms the ideas outlined in the introduction and shows that the reaction is allowed because the orbitals have the correct symmetry.

The transition state has one imaginary frequency at -955.90cm <sup>-1</sup> which corresponds to the transition state's synchronous formation of the two bonds, unlike the lowest positive frequency which is asynchronous.
[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

==The Reaction of Maleic Anhydride and 1, 3 Cyclohexadiene==

This reaction will be used to find out which conformer, endo or exo, is the most stable, and the major product in the reaction.

[[File:Endo_exo_jb.png|300px]]
Both Maleic Anhydride <ref>{{DOI|10042/to-12422}} </ref> and 1, 3 Cyclohexadiene <ref> {{DOI|10042/to-12423}} </ref> were optimised using HF/3-21G.

===The TS===

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:
====Endo====

{| class=wikitable
|-
|File Name || MA_derivativefrequency
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -0.05150479
|-
|RMS Gradient Norm (a.u.) || 0.00000664
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye) || 6.1664
|-
|Point Group ||
|-
| || {{DOI|10042/to-12458 }}
|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.
TS imaginary frequency:

[[File:Ts movement jb.gif|TS movement - Endo]]

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

====Exo====

The other conformer was produced in the same way and the files are referenced <ref>{{DOI|10042/to-12556}} </ref> <ref> {{DOI|10042/to-12557}} </ref>.

{| class=wikitable
|-
| ||opt derivative bond
|-
|File Name || checkpoint_55865(1)
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.) || -0.05041982
|-
|RMS Gradient Norm (a.u.) || 0.00001951
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 5.5645
|-
|Point Group ||
|}

A negative frequency at -812.28cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

TS imaginary frequency:

[[File:Ts_movement_oc_jb.gif| TS movement - Exo]]

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. As with the other conformer, the double bond is longer than expected at 1.39A. The single bond is also the same as in the other conformer. The distance between Maleic Anhydride and 1, 3 Cyclohexadiene is a little longer at 2.17A. This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

====Conclusion====

Now that both conformers have been optimised we are able to conclude which is the most stable.

{| class=wikitable

|-

| || Exo || Endo

|-

| Total Energy (a.u.) || -0.05041982 || -0.05150479

|}
As you can see from the table, the endo form is the most stable by 0.001085 Hartrees, which is 0.68 kcal/mol. This is most likely due to the exo structure suffering from steric strain between the carbonyl carbons and the 1, 3, cyclohexadiene ring. In addition, secondary orbital overlap accounts for the stability of the endo form. <ref> M. Anne Fox, R. Cardona, and N. J. Kiwie, J . Org. Chem. 1987,52, 1469-1474 </ref>. This can be observed n their molecular orbitals.

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T16:00:33Z

Jgb09: /* The TS */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Hexadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 hexadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

===Butadiene===

====Optimisation====

Butadiene was optimised using the AM1 semi-empirical method<ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>:

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene - Symmetric, B2''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene - Asymmetric, A2''']]

Cis Butadiene has C<sub>2V</sub> symmetry and its HOMO is asymmetric with respect to its principle plane of symmetry and was chosen over trans because it gives a better orbital overlap.

The below picture shows the plane of symmetry present in the molecular orbitals:

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

===The envelope===

The transition state structure resembles an envelope with ethene approaching butadiene from above.

To optimise the structure the freeze bond method was applied.
The first structure obatined by freezing the coordinates is here: {{DOI|10042/to-12420}}

The final structure of the transition state is here: {{DOI|10042/to-12421}}

The HOMO and LUMO of the transition structure are outlined below:

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

As you can see from the diagram, the HOMO consists of two σ-bonds formed through the overlap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene. The LUMO is formed of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene. This confirms the ideas outlined in the introduction and shows that the reaction is allowed because the orbitals have the correct symmetry.

The transition state has one imaginary frequency at -955.90cm <sup>-1</sup> which corresponds to the transition state's synchronous formation of the two bonds, unlike the lowest positive frequency which is asynchronous.
[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

==The Reaction of Maleic Anhydride and 1, 3 Cyclohexadiene==

This reaction will be used to find out which conformer, endo or exo, is the most stable, and the major product in the reaction.

[[File:Endo_exo_jb.png|300px]]
Both Maleic Anhydride <ref>{{DOI|10042/to-12422}} </ref> and 1, 3 Cyclohexadiene <ref> {{DOI|10042/to-12423}} </ref> were optimised using HF/3-21G.

===The TS===

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable
|-
|File Name || MA_derivativefrequency
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -0.05150479
|-
|RMS Gradient Norm (a.u.) || 0.00000664
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye) || 6.1664
|-
|Point Group ||
|-
| || {{DOI|10042/to-12458 }}
|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.
TS imaginary frequency:

[[File:Ts movement jb.gif|TS movement]]

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

The other conformer was produced in the same way and the files are referenced <ref>{{DOI|10042/to-12556}} </ref> <ref> {{DOI|10042/to-12557}} </ref>.

{| class=wikitable
|-
| ||opt derivative bond
|-
|File Name || checkpoint_55865(1)
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.) || -0.05041982
|-
|RMS Gradient Norm (a.u.) || 0.00001951
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 5.5645
|-
|Point Group ||
|}

A negative frequency at -812.28cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

TS imaginary frequency:

[[File:Ts_movement_oc_jb.gif| TS movement]]

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. As with the other conformer, the double bond is longer than expected at 1.39A. The single bond is also the same as in the other conformer. The distance between Maleic Anhydride and 1, 3 Cyclohexadiene is a little longer at 2.17A. This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T15:59:34Z

Jgb09: /* The Diels Alder Cycloaddition */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Hexadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 hexadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

===Butadiene===

====Optimisation====

Butadiene was optimised using the AM1 semi-empirical method<ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>:

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene - Symmetric, B2''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene - Asymmetric, A2''']]

Cis Butadiene has C<sub>2V</sub> symmetry and its HOMO is asymmetric with respect to its principle plane of symmetry and was chosen over trans because it gives a better orbital overlap.

The below picture shows the plane of symmetry present in the molecular orbitals:

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

===The envelope===

The transition state structure resembles an envelope with ethene approaching butadiene from above.

To optimise the structure the freeze bond method was applied.
The first structure obatined by freezing the coordinates is here: {{DOI|10042/to-12420}}

The final structure of the transition state is here: {{DOI|10042/to-12421}}

The HOMO and LUMO of the transition structure are outlined below:

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

As you can see from the diagram, the HOMO consists of two σ-bonds formed through the overlap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene. The LUMO is formed of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene. This confirms the ideas outlined in the introduction and shows that the reaction is allowed because the orbitals have the correct symmetry.

The transition state has one imaginary frequency at -955.90cm <sup>-1</sup> which corresponds to the transition state's synchronous formation of the two bonds, unlike the lowest positive frequency which is asynchronous.
[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

==The Reaction of Maleic Anhydride and 1, 3 Cyclohexadiene==

This reaction will be used to find out which conformer, endo or exo, is the most stable, and the major product in the reaction.

[[File:Endo_exo_jb.png|300px]]
Both Maleic Anhydride <ref>{{DOI|10042/to-12422}} </ref> and 1, 3 Cyclohexadiene <ref> {{DOI|10042/to-12423}} </ref> were optimised using HF/3-21G.

===The TS===

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable
|-
|File Name || MA_derivativefrequency
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -0.05150479
|-
|RMS Gradient Norm (a.u.) || 0.00000664
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye) || 6.1664
|-
|Point Group ||
|-
| || {{DOI|10042/to-12458 }}
|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.
TS imaginary frequency:

[[File:Ts movement jb.gif|TS movement]]

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

The other conformer was produced in the same way and the files are referenced <ref>{{DOI|10042/to-12556}} </ref> <ref> {{DOI|10042/to-12557}} </ref>.

{| class=wikitable
|-
| ||opt derivative bond
|-
|File Name || checkpoint_55865(1)
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RAM1
|-
|Basis Set || ZDO
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.) || -0.05041982
|-
|RMS Gradient Norm (a.u.) || 0.00001951
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 5.5645
|-
|Point Group ||
|}

A negative frequency at -812.28cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

TS imaginary frequency:

[[

File:Ts_movement_oc_jb.gif| TS movement]]

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and Maleic Anhydride and 1, 3 Cyclohexadiene. As with the other conformer, the double bond is longer than expected at 1.39A. The single bond is also the same as in the other conformer. The distance between Maleic Anhydride and 1, 3 Cyclohexadiene is a little longer at 2.17A. This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T15:37:36Z

Jgb09: /* The Diels Alder Cycloaddition */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Hexadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 hexadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

==Butadiene==

===Optimisation===

Butadiene was optimised using the AM1 semi-empirical method<ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>:

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene - Symmetric, B2''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene - Asymmetric, A2''']]

Cis Butadiene has C<sub>2V</sub> symmetry and its HOMO is asymmetric with respect to its principle plane of symmetry and was chosen over trans because it gives a better orbital overlap.

The below picture shows the plane of symmetry present in the molecular orbitals:

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

====The envelope====

The transition state structure resembles an envelope with ethene approaching butadiene from above.

To optimise the structure the freeze bond method was applied.
The first structure obatined by freezing the coordinates is here: {{DOI|10042/to-12420}}

The final structure of the transition state is here: {{DOI|10042/to-12421}}

The HOMO and LUMO of the transition structure are outlined below:

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

As you can see from the diagram, the HOMO consists of two σ-bonds formed through the overlap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene. The LUMO is formed of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene. This confirms the ideas outlined in the introduction and shows that the reaction is allowed because the orbitals have the correct symmetry.

The transition state has one imaginary frequency at -955.90cm <sup>-1</sup> which corresponds to the transition state's synchronous formation of the two bonds, unlike the lowest positive frequency which is asynchronous.
[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

==The Reaction of Maleic Anhydride and 1, 3 Cyclohexadiene==

This reaction will be used to find out which conformer, endo or exo, is the most stable, and the major product in the reaction.

[[File:Endo_exo_jb.png|300px]]
Both Maleic Anhydride <ref>{{DOI|10042/to-12422}} </ref> and 1, 3 Cyclohexadiene <ref> {{DOI|10042/to-12423}} </ref> were optimised using HF/3-21G.

===The TS===

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable

|-

|File Name || MA_derivativefrequency
|-

|File Type || .fch
|-

|Calculation Type || FREQ
|-

|Calculation Method || RAM1
|-

|Basis Set || ZDO
|-

|Charge || 0
|-

|Spin || Singlet
|-

|Total Energy (a.u.)|| -0.05150479

|-

|RMS Gradient Norm (a.u.) || 0.00000664
|-

|Imaginary Freq ||

|-

|Dipole Moment (Debye) || 6.1664

|-

|Point Group ||

|-

| || {{DOI|10042/to-12458 }}

|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and molecule 1 and 2. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

TS movement:

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

File:Endo exo jb.png

2012-02-18T15:36:55Z

Jgb09:

Rep:Mod:mod3 jb

2012-02-18T14:47:34Z

Jgb09:

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Hexadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 hexadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

==Butadiene==

===Optimisation===

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> -Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

===MO analysis===

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The TS====

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable

|-

|File Name || MA_derivativefrequency
|-

|File Type || .fch
|-

|Calculation Type || FREQ
|-

|Calculation Method || RAM1
|-

|Basis Set || ZDO
|-

|Charge || 0
|-

|Spin || Singlet
|-

|Total Energy (a.u.)|| -0.05150479

|-

|RMS Gradient Norm (a.u.) || 0.00000664
|-

|Imaginary Freq ||

|-

|Dipole Moment (Debye) || 6.1664

|-

|Point Group ||

|-

| || {{DOI|10042/to-12458 }}

|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and molecule 1 and 2. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

TS movement:

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T14:45:26Z

Jgb09: /* The Diels Alder Cycloaddition */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=

The Diels Alder Cycloaddition is one of the most widely used techniques, giving stereo specific and regio controlled products is a pericyclic reaction in which a diene and a dienophile combine to give a six membered ring. <ref name=da>Francesco Fringuelli, Aldo Taticch, The Diels-Alder reaction: selected practical methods, 1988 </ref>. In order for the reaction to occur, the reagents need to have orbitals with the same symmetry so that overlap of orbitals can occur. The reaction is also accelerated if the diene is electron donating and the dienophile electron withdrawing <ref name=da></ref>.

==Optimising Diels Alder==

The reaction between ethene and butadiene is an excellent example of a Diels Alder, and will be used to illustrate the above points. In order to compute its transition state, one must first optimise ethene and butadiene separately.

===Ethene===

Ethene was optimised using standard AM1 semi empirical methods: {{DOI|10042/to-12522}}

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The TS====

In order to find the transition state of the reaction the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unfrozen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable

|-

|File Name || MA_derivativefrequency
|-

|File Type || .fch
|-

|Calculation Type || FREQ
|-

|Calculation Method || RAM1
|-

|Basis Set || ZDO
|-

|Charge || 0
|-

|Spin || Singlet
|-

|Total Energy (a.u.)|| -0.05150479

|-

|RMS Gradient Norm (a.u.) || 0.00000664
|-

|Imaginary Freq ||

|-

|Dipole Moment (Debye) || 6.1664

|-

|Point Group ||

|-

| || {{DOI|10042/to-12458 }}

|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and molecule 1 and 2. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between molecule 1 and 2 is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

Both molecular orbitals are antisymmetric.

TS movement:

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T14:21:19Z

Jgb09: /* The Envelope TS */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

In order to find the transition state of the "envelope" the freeze bond method was applied. First the co ordinates of the carbons where bond breaking and moaking would occur were frozen and the geometry optimised: {{DOI|10042/to-12461 }}. Then they were unforzen and set to derivative, and the TS(Berny) optimisation selected. The following table displays the result:

{| class=wikitable

|-

|File Name || MA_derivativefrequency
|-

|File Type || .fch
|-

|Calculation Type || FREQ
|-

|Calculation Method || RAM1
|-

|Basis Set || ZDO
|-

|Charge || 0
|-

|Spin || Singlet
|-

|Total Energy (a.u.)|| -0.05150479

|-

|RMS Gradient Norm (a.u.) || 0.00000664
|-

|Imaginary Freq ||

|-

|Dipole Moment (Debye) || 6.1664

|-

|Point Group ||

|-

| || {{DOI|10042/to-12458 }}

|}

A negative frequency at -806.42 cm <sup>-1</sup> was found and the vibration corresponded to that of the transition state.

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

The above Jmol displays bond lengths between the C=C, C-C and the ethylene and butadiene. Typical sp2-sp2 carbon double bond lengths are between 1.31 and 1.34A, and single sp3 to sp2 are of the order of 1.49 - 1.52A<ref> Eric V. Anslyn, Dennis A. Doughert, Modern physical organic chemistry, 2006 </ref>. The double bond displayed is 1.39A which is more like that found in arenes, possibly alluding to the bond having aromatic character. The single bond is as expected at 1.49A. The distance between butadiene and ethene is 2.16A, which suggests it is not bonded yet. The van der waal radius of carbon is poorly defined but is believed to be in the region of 1.7-2.1A. The fitting of graphite suggests it is closest to 1.9A. <ref>Victor Gold, Advances in physical organic chemistry, Volume 13, 1976</ref> This suggests the the partly formed σ C-C bonds in the TS are just out of the van der waal radius, and are not quite bonded.

The two pictures below are the HOMO and LUMO of the transition state.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - Symmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - Antisymmetric]]

The LUMO is symmetric and the HOMO antisymmetric.

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T13:13:22Z

Jgb09: /* Optimising the Reactants and Products */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects<ref>Henry Rzepa, 2<sup>nd</sup> Year Course, Conformational Analysis</ref>.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T13:10:01Z

Jgb09: /* Optimising the Reactants and Products */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability. The fact that gauche suffers from steric strain would suggest it is less stable than anti, and it surprising that Gauche 3 is the most stable. NBO analysis would shed light on this.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-18T12:51:10Z

Jgb09: /* Comparison of "Chair" and "Boat" */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T17:00:53Z

Jgb09: /* Optimisation */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

Butadiene was optimised using the AM1 semi-empirical method

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref> - Symmetric''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref> - Asymmetric''']]

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:59:24Z

Jgb09: /* Optimisation */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mobut>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mobut></ref>''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:59:13Z

Jgb09: /* Optimisation */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref name=mo but>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene<ref name=mo but></ref>''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:57:47Z

Jgb09: /* Optimisation */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene <ref>https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG </ref>''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:54:14Z

Jgb09: /* Comparison of "Chair" and "Boat" */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

'''Boat'''

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12343}} Energy = -231.67506412''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12344}} Energy = -231.68440451''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

'''Chair'''

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12403}} Energy = -231.68603300''']]

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12404}} Energy = -231.69166400''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

'''Chair - Points = 100'''

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300''']]

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12408}} Energy = -231.69166400''']]

For chair, 100 points gave identical energies to using 50.

'''Boat- Points = 70'''

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''FC = once {{DOI|10042/to-12405}} Energy = -231.67506412''']]

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:49:53Z

Jgb09: /* Comparison of "Chair" and "Boat" */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

Boat - IRC FC = once {{DOI|10042/to-12343}} Energy = -231.67506412

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

Boat - IRC FC = always {{DOI|10042/to-12344}} Energy = -231.68440451

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

chair - IRC FC = once {{DOI|10042/to-12403}} Energy = -231.68603300

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}} Energy = -231.69166400

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum. This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}} Energy = -231.69166400

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

For chair, 100 points gave identical energies to using 50.

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}} Energy = -231.67506412

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Increasing the points to 70 for boat gives the same energy for force constant once but force constant always gives a structure that seems to have veered off the path.

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:45:01Z

Jgb09: /* Comparison of "Chair" and "Boat" */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

On comparing chair and boat energies, it can be seen that the chair conformer is stable by approximately 10kcal/mol.

COMPARE BOND LENGTHS IN EACH

The Intrinsic Reaction Coordinate or IRC method was employed and the graphs are displayed below for comparison:

Boat - IRC FC = once {{DOI|10042/to-12343}} Energy = -231.67506412

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

This graph contained 24 iterations, and the last point does not seem to be a minimum because the gradient of the graph has not become close to 0.

Boat - IRC FC = always {{DOI|10042/to-12344}} Energy = -231.68440451

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

This graph had 51 iterations, and the gradient converged to 0, meaning a minimum was obtained. Having the force constant calculated at every iteration leads to a greater number of iterations and a lower energy being calculated.

chair - IRC FC = once {{DOI|10042/to-12403}} Energy = -231.68603300

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}} Energy = -231.69166400

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Again using force constant set to always gives a lower energy. Comparing boat and chair, chair comes out as the most stable conformer in both methods.

The IRC were restarted and a larger number of points specified to obtain a minimum:

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }} Energy = -231.68603300

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}} Energy = -231.69166400

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}} Energy = -231.67506412

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }} Energy = -231.69213482

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

This method gives more reliable energies but can sometimes lead to the wrong structure being computed if too many points are specified.

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:05:47Z

Jgb09: /* Optimising the "Chair" Transition Structures */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

Both methods produced a nearly identical energy and imaginary frequency.

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:04:20Z

Jgb09: /* Optimising Boat Transition Structure */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0<sup>o</sup>.

The inside C-C-C to 100<sup>o</sup>.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T16:03:50Z

Jgb09: /* Optimising Boat Transition Structure */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

==Optimising Boat Transition Structure==

The QST2 method was used to find the boat transition structure. This method interpolates between a specified reactant and product to find the structure between the two.

The conformer of Anti 2 was used and the reactants and products numbered appropriately. If submitted the job fails because the molecules are not close enough to the transition state structure, and QST2 does not consider rotation around the central bonds. To solve this problem, the dihedral angles were altered as outlined below:

The central C-C-C-C dihedral angle to 0o.

The inside C-C-C to 100o.

The QST2 calculation then converged to the boat transition structure and one imaginary frequency of -839.73 was obtained.

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|10042/to-12338}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T15:44:51Z

Jgb09: /* Optimising the "Chair" Transition Structures */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

The chair was then minimised in an alternate way, using the freeze bond method. The co ordinates of the bond breaking/making carbons were frozen, the geometry optimised, then unfrozen, set as derivatives and reoptimised.

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RHF||RHF
|-
|Basis Set|| 3-21G || 3-21G
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||-231.61518422|| -231.61932190
|-
|RMS Gradient Norm (a.u.)||0.00326607|| 0.00005539
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0017|| 0.0000
|-
|Point Group || C1 ||
|-
| ||{{DOI| 10042/to-12611 }} || {{DOI|10042/to-12618}}
|}

The imaginary frequency is -817.86 and is displayed below:

[[File:Imagi_freq_jb.gif]]

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

File:Imagi freq jb.gif

2012-02-17T15:44:40Z

Jgb09:

Rep:Mod:mod3 jb

2012-02-17T15:29:47Z

Jgb09: /* Optimising the "Chair" Transition Structures */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

It was then minimised by two different methods.

Firstly, using HF/3-21G and optimising to a TS (Berny). The force constant was caluclated once and Opt=NoEigen entered into key words to stop the program crashing if more than one imaginary frequency is found. The results are below:

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

The imaginary peak, shown below, was at -817.95, which indicates the correct minimum was reached.

[[File:Istretch_jb.gif‎]]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

"redundant" opt

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

File:Istretch jb.gif

2012-02-17T15:29:06Z

Jgb09:

Rep:Mod:mod3 jb

2012-02-17T15:15:14Z

Jgb09: /* Optimising the "Chair" Transition Structures */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Dipole Moment (Debye)||0.0003
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

"redundant" opt

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T15:14:06Z

Jgb09: /* Optimising the "Chair" Transition Structures */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

The Chair transition structure was optimised by first optimising an allyl CH<sub>2</sub>CHCH<sub>2</sub> fragment using HF/3-21G theory then combining two of these fragments together, with the terminal carbons at a distance of 2.2A apart.

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

"redundant" opt

{| class=wikitable
|File Name||Bonds - Frozen || Bonds - Derivative
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T15:03:30Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti 2 Frequency Analysis==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T15:02:45Z

Jgb09: /* Anti 2 Opt */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

Anti 2 was optimised using two different methods. Firstly using the HF/3-21G then B3LYP/6-31G*, and the results are displayed in the table below.

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger. The overall change is very small.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:59:26Z

Jgb09: /* Optimising the Reactants and Products */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

The following data was obtained by optimising the conformers using HF/3-21G level of theory.

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

The table above displays all analysed gauche conformers, whereas the below table shows the anti.

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:56:45Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

The chair and boat transition structures were reoptimised using the B3LYP/6-31G* level of theory and frequency calculations carried out. The HF/3-21G optimized structures were used as a starting point. The below table summarises the energies obtained and compares them to the energies of Anti 2 butadiene. This enables Activation energy to be calculated and compared to experimental results.

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:49:24Z

Jgb09: /* Optimising the Reactants and Products */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o</sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:49:12Z

Jgb09: /* Optimising the Reactants and Products */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:48:22Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:47:14Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| || ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:47:01Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}} || || || ||
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790 || || || ||
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685|| || || ||
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:46:21Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat || Ea (Chair, kcal/mol) || Ea (Boat, kcal/mol)|| Exp Ea Chair|| Exp Ea Boat
|-
| || || {{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}}
|-
| Total Energy || -234.611710 || -234.556983 || -234.543079 || 34.341905 || 43.066790
|-
| Zero Point Energy || -234.469204 || -234.414929 || -234.402304 || 34.058032 || 41.980352 || 33.5 ± 0.5|| 44.7 ± 2.0
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970 || 33.163223 || 41.344685
|}

The experimental value of Ea for chair is very close to the calculated, considering the error of ± 0.5, leaving a minimum difference of 0.058 kcl/mol. The experimental value for boat is also close, but has a minimum difference of 0.72 kcal/mol.

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:34:01Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| ||{{DOI|10042/to-12469}}|| {{DOI|10042/to-12472}}
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.469204 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970
|}

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:32:51Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.469204 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.461857|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:31:32Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies = -234.469204

Sum of electronic and thermal Energies = -234.461857

Sum of electronic and thermal Enthalpies = -234.460913

Sum of electronic and thermal Free Energies = -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.416244 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.408954|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:31:08Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1731.07 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1734.31 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.469204
Sum of electronic and thermal Energies= -234.461857
Sum of electronic and thermal Enthalpies= -234.460913
Sum of electronic and thermal Free Energies= -234.500777

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.416244 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.408954|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:28:53Z

Jgb09: /* Anti 2 Opt */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12573}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.416244 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.408954|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:28:09Z

Jgb09: /* Anti 2 Opt */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G(D)
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.61171035
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00001327
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.416244 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.408954|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:19:55Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.559704 || -234.556983 || -234.543079
|-
| Zero Point Energy || -234.416244 || -234.41492903 || -234.402304
|-
| Thermal Energy ||-234.408954|| 234.409008 || 234.395970
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T14:09:51Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.55970425 || -234.55698303 || -234.54307975
|-
| Zero Point Energy || -234.41624425 || -234.41492903 || -234.40230375
|-
| Thermal Energy ||-234.408954|| -234.41492903 || -234.40230375
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T13:59:47Z

Jgb09: /* Comparison of Activation Energies */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
| || Anti 2 || Chair || Boat
|-
| Total Energy || -234.55970425 || -234.55698303 || -234.54307975
|-
| Zero Point Energy || -234.41624425 || -234.41492903 || -234.40230375
|-
| Thermal Energy ||-234.41624425 || -234.41492903 || -234.40230375
|}

|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T13:41:46Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:

Zero-point Energies= 0.143460

Thermal Correction Energies= 0.143460

Thermal Correction Enthalpies= 0.143460

Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

boat:

frequency = -532.35

opt + freq boat. thermo analysis

0.140776 zero point correction, thermal to energy, thermal to enthalpy, thermal to Gs

chair :

frequency = -565.53

thermal data:
0.142054 - zero point energy, thermal e, thermal en, thermal c to Gs

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T13:41:28Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

As you can see, both methods differ from each other and literature for their frequencies. The closest to literature is the 6-31G method.

The following energies will be used to look at activation energy:

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

Thermal Information:
Zero-point Energies= 0.143460
Thermal Correction Energies= 0.143460
Thermal Correction Enthalpies= 0.143460
Thermal Correction to Gibbs Free Energies= 0.143460

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

boat:

frequency = -532.35

opt + freq boat. thermo analysis

0.140776 zero point correction, thermal to energy, thermal to enthalpy, thermal to Gs

chair :

frequency = -565.53

thermal data:
0.142054 - zero point energy, thermal e, thermal en, thermal c to Gs

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T13:35:34Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G || Literature <ref> P. Huber-Wälchli, Hs .H. Günthard, Volume 37, Issue 5, Pages 285–304, 1980 </ref>
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63 || 1643
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000 ||
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11 || -
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920 ||
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}} ||
|}

[[File:Ir_spectra_anti2jb.jpg | 600px|alt=Alt text|3-21G ]]

[[File:IR anti2 631g full JB.jpg|300px| alt=Alt text|6-31G ]]

compare to literature

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

thermal info:
0.143460 - zero point energy, thermal correction energy, thermal correction enthalpy, thermal correction to gibbs free enrgy

COMPARE 0K TO 298K

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

boat:

frequency = -532.35

opt + freq boat. thermo analysis

0.140776 zero point correction, thermal to energy, thermal to enthalpy, thermal to Gs

chair :

frequency = -565.53

thermal data:
0.142054 - zero point energy, thermal e, thermal en, thermal c to Gs

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>

Rep:Mod:mod3 jb

2012-02-17T13:20:07Z

Jgb09: /* Anti Frequency */

Module 3 - Yr 3 Computational Lab: Jessica Bevan

=Introduction=

The aim of this module is to show how computational chemistry can be used to model transition states which lead to a greater understanding of reaction mechanisms. In order to do this, specific techniques have to be used in order to take account of the breaking and making of bonds.

=The Cope Rearrangement Tutorial=
The Cope Rearrangement is a pericyclic reaction of 1,5 diene in which a [3,3] sigmatropic rearrangment occurs as outlined in the below diagram <ref>James Ralph Hanson, Organic synthetic methods, 2002 </ref>:

[[file:Cope_mechanism_JB.bmp|‎thumb|300px|centre|alt=Alt text|'''IR Spectra''']]

The rearrangement can go through one of two transition states; chair or boat.
[[File:Diagram of chair boat.bmp|200px|Diagram illustrating chair and boat conformations]]

The exact nature of the transition state changes according to the substituents and can range from resembling two independant allyl radicals and a cyclo hexane 1, 4 di radical. This is illustrated in the below diagram <ref> László Kürti, Barbara Czak, Strategic applications of named reactions in organic synthesis: background and Detailed Mechanisms, 2005 </ref>:

[[ File:Cope_mechanism_allyl_radicals_jb.bmp|400px|Diagram illustrating the differences in TS radicals]]

In the majority of reactions, the transition state is late and the bonds between C1 and C6 are developed.

==Optimising the Reactants and Products==

Butadiene can exhibit two conformers, which each in turn can exhibit isomerisation through rotation of the CHCH<sub>2</sub> groups. The dihedral angle between the two CHCH<sub>2</sub>s for Gauche conformers is 60<sup>o</sup>, whereas Anti has a dihedral angle of 180<sup>o<sup>. All analysed possibilities are outlined below. There are a couple of others yet to be analysed.

[[File:All_conformers_jb.bmp|500px|Diagram of Gauche and Anti conformers analysed]] [[File:All_molceules_jb.PNG|800px|Snap shots of all analysed conformers]]

{| class=wikitable
| || Gauche 4 || Gauche 2 || Gauche 3 || Gauche 1 || Gauche 5
|-
|File Type ||.fch || .fch || .fch || .fch || .fch
|-
|Calculation Type||FOPT || FOPT || FOPT || FOPT || FOPT
|-
|Calculation Method||RHF || RHF || RHF || RHF || RHF
|-
|Basis Set||3-21G || 3-21G || 3-21G || 3-21G || 3-21G
|-
|Charge||0||0||0||0||0
|-
|Spin||Singlet||Singlet||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6915304|| -231.6916670 || -231.6926612 || -231.6877159 || -231.6896158
|-
|RMS Gradient Norm (a.u.) ||0.00001006||0.00000172 || 0.00000848 || 0.00006151 || 0.00000458
|-
|Dipole Moment (Debye) ||0.1281 ||0.3806 || 0.3406 || 0.4562 || 0.4438
|-
|Point Group||C2 || C2 || C1 || C2 || C1
|-
| || {{DOI|10042/to-12224}} || {{DOI|10042/to-12455}} || {{DOI|10042/to-12456}} || {{DOI|10042/to-12457}} || {{DOI|10042/to-12462}}
|}

{| class=wikitable
| ||Anti 3 || Anti 1 || Anti 2
|-
|File Type||.fch ||.fch || .fch
|-
|Calculation Type||FOPT||FOPT || FOPT
|-
|Calculation Method||RHF||RHF || RHF
|-
|Basis Set||3-21G||3-21G || 3-21G
|-
|Charge||0||0 || 0
|-
|Spin||Singlet || Singlet || Singlet
|-
|Total Energy (a.u.)||-231.6890707||-231.6926024 ||-231.69253528
|-
|RMS Gradient Norm (a.u.)|| 0.00000819 ||0.00001824 ||0.00001042
|-
|Dipole Moment (Debye) ||0.0001|| 0.2021 ||0.0003
|-
|Point Group||C2h || C2 || Ci
|-
| ||{{DOI|10042/to-12226}}|| {{DOI|10042/to-12228}} ||{{DOI|10042/to-12227}}
|}

Order of stability:

Anti 3 < Gauche 1 < Gauche 5 < Gauche 4 < Gauche 2 < Anti 2 < Anti 1 < Gauche 3

In order to understand the reasons behind the differing stabilities one has to consider three general effects.

1) Favourable interactions between sigma orbitals and sigma* orbitals.

2) Bond-bond Pauli repulsion

3) H---H interactions

In general, effect 2 disfavours and effect 3 favours gauche. Most of the time, effect 1 becomes the deciding factor in determining stability.

'''LOOK AT NBO'''

==Anti 2 Opt==

METHOD USED?

All discussed angles and lengths are picture in the jmol provided.

{| class=wikitable
|-
|File Name||anti2_opt||anti2_opt631g
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FOPT
|-
|Calculation Method||RHF|| RB3LYP
|-
|Basis Set||3-21G|| 6-31G
|-
|Charge ||0||0
|-
|Spin||Singlet||Singlet
|-
|E RHF (a.u.) ||-231.69253528||-234.55970425
|-
|RMS Gradient Norm (a.u.)||0.00001042||0.00004552
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (Debye)||0.0003 || 0.0000
|-
|Point Group||Ci||Ci
|-
|Dihedral Length (nm) || 0.354 || 0.361
|-
|Angle between CH<sub>2</sub>-CH-CH<sub>2</sub> (<sup>o</sup>) || 124.8 || 125.2
|-
|Central Dihedral Angle || 180.00 || -179.99
|-
| ||{{DOI|10042/to-12227}} || {{DOI|10042/to-12229}}
|-
| || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 3-21G </text>
</jmolAppletButton>
</jmol> || <jmol>
<jmolAppletButton>
<uploadedFileContents>Anti2 opt631g jb.mol</uploadedFileContents>
<script> measure 14 6; measure 1 4 6 </script><text>Click here for Jmol of 6-31G</text>
</jmolAppletButton>
</jmol>
|}

Comparing the dihedral lengths on each it can be seen that the method using 6-31G gives a longer molecule. This is because the angle between CH<sub>2</sub>-CH-CH<sub>2</sub> is bigger.

==Anti Frequency ==

{| class=wikitable
|Method || 3-21G || 6-31G
|-
| Symmetric C=C Frequency (cm <sup>-1</sup>) ||1855.58|| 1724.63
|-
| Symmetric C=C Intensity || 0.0008 || 0.0000
|-
| Asymmetric C=C Frequency (cm <sup>-1</sup>)||1858.09|| 1728.11
|-
| Asymmetric C=C Intensity || 16.8650 || 19.4920
|-
| || {{DOI|10042/to-12562}} ||{{DOI|10042/to-12230}}
|}

[[File:Ir_spectra_anti2jb.jpg | 600px|alt=Alt text|3-21G ]]

[[File:IR anti2 631g full JB.jpg|300px| alt=Alt text|6-31G ]]

compare to literature

Sum of electronic and zero-point Energies= -234.416244
Sum of electronic and thermal Energies= -234.408954
Sum of electronic and thermal Enthalpies= -234.408010
Sum of electronic and thermal Free Energies= -234.447849

thermal info:
0.143460 - zero point energy, thermal correction energy, thermal correction enthalpy, thermal correction to gibbs free enrgy

COMPARE 0K TO 298K

==Optimising the "Chair" Transition Structures==

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RHF
|-
|Basis Set||3-21G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -231.61932239
|-
|RMS Gradient Norm (a.u.)||0.00002067
|-
|Imaginary Freq ||
|-
|Dipole Moment (Debye)||0.0003
|-
|Point Group||
|-
| ||{{DOI|10042/to-12236}}
|}

opt for opt=noeigen

imaginary peak = -817.95

[[Media:Imaginarystretchmovie_JB.mng|'''Movie depicting the imaginary stretch''']]

[[File:IR spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

[[File:Raman Activity Spectrum JB.jpg|thumb|750px|centre|alt=Alt text|'''Raman Activity Spectrum''']]

[[File:U depolarisation Spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''U-Depolarisation Spectrum''']]

[[File:P Depolarisation spectra JB.jpg|thumb|750px|centre|alt=Alt text|'''P-Depolarisation Spectrum''']]

"redundant" opt

{| class=wikitable
|File Name||opt_char_redundant||opt_chair_2ndredundant
|-
|File Type||.log||.fch
|-
|Calculation Type||FOPT||FTS
|-
|Calculation Method||RAM1||RAM1
|-
|Basis Set||ZDO||ZDO
|-
|Charge||0||0
|-
|Spin||Singlet||Singlet
|-
|E(RAM1)(a.u.)||0.10684773||0.10683176
|-
|RMS Gradient Norm (a.u.)||0.00449397||0.00449397
|-
|Imaginary Freq|| ||
|-
|Dipole Moment (debye)||0.0012|| 0.0010
|-
|Point Group || C1 ||
|-
| ||{{DOI|10042/to-12249}} || {{DOI|10042/to-12250}}
|}

COMPARE METHODS - 2ND ENERGY LOOKS WRONG!!

==Optimising Boat Transition Structure==

used optimised Ci

labelled atoms as required

opt+freq TS(QST2) failed - DOESNT CONSIDER ROTATION AROUND CENTRE BONDS

adjusted angles

opt+freq TS(QST2) worked - boat structure appeared

imaginary frequencies = -839.73

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RHF
|-
|Basis Set ||
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -231.60280227
|-
|RMS Gradient Norm (a.u.) || 0.00003242
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.1583
|-
|Point Group ||
|-
| || {{DOI|}}
|}

[[File:Imaginary_qrt2_movie_jb.gif|'''Movie depicting the imaginary stretch''']]

[[File:IR JB boat.jpg|thumb|750px|centre|alt=Alt text|'''IR Spectra''']]

==Comparison of "Chair" and "Boat"==

WHICH IS MORE STABLE???

COMPARE BOND LENGTHS IN EACH

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

Intrinsic Reaction Coordinate or IRC method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Boat - IRC FC = once {{DOI|10042/to-12343}}

24

[[File:Full diagram boat once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC FC = always {{DOI|10042/to-12344}}

51

[[File:Full diagram always boat JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE ONCE AND ALWAYS

chair - IRC FC = once {{DOI|10042/to-12403}}

45

[[File:Total Energy diagram once jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

chair - IRC FC = always {{DOI|10042/to-12404}}

93

[[File:Total Energy Diagram always jb.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE BOAT AND CHAIR

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure

Chair - IRC 100 FC = once {{DOI|10042/to-12407 }}

45

[[File:Total Energy Diagram once 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Chair - IRC 100 FC = always {{DOI|10042/to-12408}}

93

[[File:Total Energy Diagram always 100 jb.jpg|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 iterations FC = once {{DOI|10042/to-12405}

23

[[File:Full diagram 70 once JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

Boat - IRC 70 FC = always {{DOI|10042/to-12406 }}

71

[[File:Full energy diagram 70 always JB.png|thumb|500px|centre|alt=Alt text|'''Energy change diagram''']]

COMPARE INCREASING ITTERATIONS

DID ALL REACH A MINIMUM??

===Comparison of Activation Energies===

reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures

boat:

optimised using 6-31G and calculated frequency:

{| class=wikitable
|-
|File Name ||
|-
|File Type || .fch
|-
|Calculation Type || FREQ
|-
|Calculation Method || RB3LYP
|-
|Basis Set || 6-31G(D)
|-
|Charge || 0
|-
|Spin || Singlet
|-
|Total Energy (a.u.)|| -234.54307975
|-
|RMS Gradient Norm (a.u.) || 0.00000516
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye) || 0.0607
|-
|Point Group ||
|-
| || {{DOI|10042/to-12472}}
|}

chair:

optimising using 6-31G with frequency analysis

{| class=wikitable
|-
|File Name||OPT_FREQ
|-
|File Type||.fch
|-
|Calculation Type||FREQ
|-
|Calculation Method||RB3LYP
|-
|Basis Set||6-31G
|-
|Charge||0
|-
|Spin||Singlet
|-
|Total Energy (a.u.) || -234.55698303
|-
|RMS Gradient Norm (a.u.)||0.00001245
|-
|Imaginary Freq || 1
|-
|Dipole Moment (Debye)||0.0000
|-
|Point Group||
|-
| ||{{DOI|10042/to-12469}}
|}

Used Gauss View FrkChk

boat:

frequency = -532.35

opt + freq boat. thermo analysis

0.140776 zero point correction, thermal to energy, thermal to enthalpy, thermal to Gs

chair :

frequency = -565.53

thermal data:
0.142054 - zero point energy, thermal e, thermal en, thermal c to Gs

CONVERT TO KCAL/MOL

compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

(Convert hartree into kcal and compare)

If you take the values computed at 0 K, how close are they to the experimental values?

=Butadiene=

POINT GROUP OF BUTADIENE

EXPLAIN A AND S

==Optimisation==

AM1 opt

https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BUTA_FOR_OPT_jb.LOG

[[File:LUMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Butadiene''']]

[[File:HOMO but jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Butadiene''']]

LABEL SYMMETRY

==MO analysis==

[[File:Homo_lumo_symmetry_comparison_jb.jpg|thumb|200px|centre|alt=Alt text|'''Symmetry analysis''']]

Butadeien = C2V

HOMO - A2

LUMO - B2

=The Diels Alder Cycloaddition=
allyl opt: {{DOI|10042/to-12234}}

==Optimising Diels Alder==

===Ethene===

{{DOI|10042/to-12522}}

ethene = d2h

A OR S

MOS

====The envelope====

envelope 1st opt bonds frozen

{{DOI|10042/to-12420}}

envelope opt no freeze, diverge?? {{DOI|10042/to-12421}}

[[File:LUMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''LUMO of Diels Alder TS - Symmetric''']]

[[File:HOMO DA jb.jpg|thumb|200px|centre|alt=Alt text|'''HOMO of Diels Alder TS - Antisymmetric''']]

HOMO - two σ-bonds by the olap of the antisymmetric HOMO orbital of cis-butadiene with the antisymmetric LUMO of ethylene

LUMO - OLap of the symmetric HOMO of ethylene with the symmetric LUMO of cis-butadiene

COMPARE BOND LEGTHS IN BUTADIENE TO ENVELOPE TO LITERATURE

CHANGE IN HYBRIDISATION

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

imaginary frequency at -955.90 corresponds to TS

[[File:Movie_imaginary_ts_jb.gif|TS frequency]]

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

===Maelic Anhydride===

THE REACTION

USES

DIAGRAM

EXO, ENDO

op2 - {{DOI|10042/to-12422}}

op1 - {{DOI|10042/to-12423}}

====The Envelope TS====

MA freeze bond - {{DOI|10042/to-12461 }}

MA - bond derivative + frequency - {{DOI|10042/to-12458 }}

opt derivative
File Name MA_derivativefrequency
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05150479 a.u.
RMS Gradient Norm 0.00000664 a.u.
Imaginary Freq
Dipole Moment 6.1664 Debye
Point Group

negative frequency -806.42

[[Image:MA derivative jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>MA derivativefrequency JB.mol2</uploadedFileContents>
<script> measure 4 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

C=C = 0.139nm
C-C = 0.149nm
C---C = 0.216nm

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

[[Image:LUMO MA jb.png|thumb|center|150px|LUMO - antisymmetric]]

[[Image:HOMO MA jb.png|thumb|center|150px|HOMO - antisymmetric]]

TS movement

[[File:Ts movement jb.gif|TS movement]]

other conformer:

Freeze bond: {{DOI|10042/to-12556}}

Derivative: {{DOI|10042/to-12557}}

opt derivative bond
File Name checkpoint_55865(1)
File Type .fch
Calculation Type FREQ
Calculation Method RAM1
Basis Set ZDO
Charge 0
Spin Singlet
Total Energy -0.05041982 a.u.
RMS Gradient Norm 0.00001951 a.u.
Imaginary Freq 1
Dipole Moment 5.5645 Debye
Point Group

imaginary frequency = -812.28

[[Image:MA oc picture jb.png|thumb|center|150px|TS of maleic anhydride<br clear="all" />
<jmol>
<jmolAppletButton>
<uploadedFileContents>Freq derivative oc jb.mol2</uploadedFileContents>
<script> measure 5 14; measure 1 5; measure 14 15 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]]<br clear="all" />

[[File:Ts_movement_oc_jb.gif| TS movement]]

C=C = 0.139nm C-C = 0.149nm C---C = 0.217nm

COMPARE ENERGIES OF COMFORMERS

WHICH IS KINETIC/ THERMO??

IRC IF TIME

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time. (e.g. DOI:10.1021/jo0348827 )

=References=

<references/>