ChemWiki - User contributions [en]

Rep:Mod:jlphyswik

2009-11-13T14:39:17Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy was -605.7187a.u. and the imaginary vibrational frequency was at -533.9cm-1.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a longer length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because in the endo form the bridge only interferes with the hydrogens from the section that were on the furan, whereas in the exo form the entire furan ring is in this place causing a greater degree of unfavourable steric interactions.

The endo transition state is also favoured over the exo transition state due to secondary orbital overlap. In the endo transition state the carbonyl groups on the maleic anhydride are also able to contribute favourably to the partially formed σ bonds, thus stabilising them, which is why the partially formed bonds are shorter in the endo form, and another reason for the endo transition state being lower in energy, which in turn causes the preference for the endo product over the exo product. This can be shown in the image<ref>http://commons.wikimedia.org/wiki/File:Cyclopentadiene_Maleic_Anhydride_Diels_Alder.png</ref> below.

{|
| [[Image:jlphyssecondaryorbital.jpg|400px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || -605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in energies between the product and transition state however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

The imaginary vibration is at a lower frequency for the endo transition state. This would indicate that the reaction pathway from the transition state to the product requires less energy, again showing this pathway is energetically favoured.

=References=
<references/>

File:Jlphyssecondaryorbital.jpg

2009-11-13T14:39:07Z

Jl807:

Rep:Mod:jlphyswik

2009-11-13T14:23:34Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy was -605.7187a.u. and the imaginary vibrational frequency was at -533.9cm-1.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a longer length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because in the endo form the bridge only interferes with the hydrogens from the section that were on the furan, whereas in the exo form the entire furan ring is in this place causing a greater degree of unfavourable steric interactions.

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || -605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in energies between the product and transition state however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

The imaginary vibration is at a lower frequency for the endo transition state. This would indicate that the reaction pathway from the transition state to the product requires less energy, again showing this pathway is energetically favoured.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T14:21:06Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a longer length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because in the endo form the bridge only interferes with the hydrogens from the section that were on the furan, whereas in the exo form the entire furan ring is in this place causing a greater degree of unfavourable steric interactions.

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in energies between the product and transition state however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

The imaginary vibration is at a lower frequency for the endo transition state. This would indicate that the reaction pathway from the transition state to the product requires less energy, again showing this pathway is energetically favoured.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T14:13:46Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a longer length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in energies between the product and transition state however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

The imaginary vibration is at a lower frequency for the endo transition state. This would indicate that the reaction pathway from the transition state to the product requires less energy, again showing this pathway is energetically favoured.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T14:07:35Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a longer length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:56:04Z

Jl807: /* Activation Energies */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form.

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:55:26Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:36:29Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

The endo form is less strained than the exo form. This is because

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:32:01Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A, vdw radius 1.7A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:29:36Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule. Again this means that the molecular orbitals involved in the reaction must be of 'a' symmetry, which in this Diels Alder reaction corresponds to the HOMO of the maleic anhydride and the LUMO of cyclohexadiene(shown below).

{|
| [[Image:jlphysTS4HOMOplane.jpg|350px|thumb| endo transition state HOMO]]
| [[Image:jlphysmalhomo.jpg|350px|thumb| Maleic anhydride HOMO]]
| [[Image:jlphysdieneLUMO.jpg|350px|thumb| diene LUMO]]
|}

To find the transition state for molecule 3(exo) I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

File:JlphysdieneLUMO.jpg

2009-11-13T13:29:06Z

Jl807:

File:Jlphysmalhomo.jpg

2009-11-13T13:28:50Z

Jl807:

File:JlphysTS4HOMOplane.jpg

2009-11-13T13:28:27Z

Jl807:

Rep:Mod:jlphyswik

2009-11-13T13:13:04Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

The HOMO is the molecular orbital of more interest for the same reasons as those mentioned in the first DA section. It can be seen that the HOMO is 'a' symmetric in the transition state of the endo molecule.

To find the transition state for molecule 3 I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:02:23Z

Jl807:

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

=References=
<references/>

Rep:Mod:jlphyswik

2009-11-13T13:01:10Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring, replacing the furan ring with the hydrogens and vice-versa. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

Rep:Mod:jlphyswik

2009-11-13T12:55:47Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|600px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

Rep:Mod:jlphyswik

2009-11-13T12:53:12Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg||thumb|400px|note TS4 (endo is on the left)]]
|}

The exo transition state has partly formed σ bonds of a shorter length than in the endo transition state. This is a reason for the exo transition state being lower in energy. In both cases the partly formed σ bonds are longer than a usual length for fully formed σ bonds, and the closer to the normal length the partially formed bonds are the lower in energy they will be. One reason for this is that the orbital overlap between the ethene HOMO and the LUMO of the cyclohexa-1,3-diene will be poorer, resulting in a more diffuse orbital corresponding to the new σ bonds. More diffuse orbitals will result in a higher energy system, and in the endo transition state the orbitals in question are indeed more diffuse.

{|
| [[Image:jlphysdabondmos2.jpg|thumb|300px]]
|}

A table comparing properties of molecules and their transition states:

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

File:Jlphysdabondmos2.jpg

2009-11-13T12:52:42Z

Jl807:

File:Jlphysdabondmos.jpg

2009-11-13T12:52:21Z

Jl807:

Rep:Mod:jlphyswik

2009-11-13T12:19:20Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoschemecorrect.jpg|thumb|450px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|400px]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

File:Jlphysdastereoschemecorrect.jpg

2009-11-13T12:19:10Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T17:16:47Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

The partially formed carbon-carbon bonds in the transition state are of interest, specifically their bond lengths:

{|
| [[Image:jlphysdastereobonds.jpg|400px]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

File:Jlphysdastereobonds.jpg

2009-11-12T17:16:41Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T16:39:08Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213|| -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. Such a small difference means that the reason for the preference of the endo form cannot be thermodynamic. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then the endo form is preferred for kinetic reasons.

<references/>

Rep:Mod:jlphyswik

2009-11-12T16:21:13Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

<references/>

Rep:Mod:jlorgwik

2009-11-12T16:21:00Z

Jl807:

'''Introduction'''

The following is James Lees’ submission for the organic module of the computational chemistry lab course. The programmes used included ChemBio3D Ultra 12.0, ChemDraw Ultra 12.0, Gaussview 3.0, Microsoft Word, Microsoft Excel, EndNote X3. Gaussview 3.0 was used instead of Gaussview 5.0 as the 5.0 version was prone to crashing.

== Modelling Using Molecular Mechanics ==

=== Hydrogenation of Cyclopentadiene Dimer ===

The 2 isomers of the cyclopentadiene dimer 1(exo) and 2(endo), and the isomers of the hydrogenated dimer (3 and 4) were all created in ChemBio3D. Using MM2 molecular mechanics the structures were then optimised providing the energy contributions including: stretching (str), bending (bnd), torsion (tor), van der Waals (vdw). A comparison of these energies allows a comparison of their relative energies.

[[Image:jlcp1.jpg|thumb|400px| ]]

The endo isomer(2) is produced specifically over the exo isomer(1) which means that 2 must be the more stable. This is indeed shown in the overall energy given for the molecules, 31.8817 Kcal.mol-1 compared with 34.0063Kcal.mol-1. The lower energy of the endo isomer is mainly accounted for by a lower degree of torsional strain: 7.64545 Kcal.mol-1 compared to 9.5146 Kcal.mol-1 in the exo form, thus accounting for 87.98% of the energy difference.

Torsion is so much higher in the exo isomer because bond angles in 1 are so much further from the ideal of 105 for an sp3 carbon. A simple observation of each molecule also appears to show that 1 has its rings further twisted out of proportion than is visible in 2 resulting in higher torsional strain.

[[Image:jlcp2.jpg|thumb|600px| ]]

[[Image:jlcp3.jpg|thumb|600px| ]]

A comparison of the energies of the potential hydrogenated products of 2 shows isomer 3 to posess a lower energy (29.256Kcal.mol-1) than isomer 4(34.9661 Kcal.mol-1). The largest discrepancy between the isomers in this case is that 4 has a far higher result for the bending energy (19.1509) compared to 3 (13.0418) meaning it is being considerably further bent from the ‘norm’. This results in 4 being the less stable isomer and the much less likely product of the hydrogenation.

Knowing this we can say the double bond on the right hand side of the diagram of molecule 2 is less likely to be attacked during hydrogenation resulting in a reaction that selectively produces isomer 3. Considering that it is stated in the project notes that molecule 2 is favoured over 1 almost entirely, and the difference in energy between 1 and 2 is less so than for 3 and 4, it is reasonable to assume 3 will be the predominant product and as it is the thermodynamically more stable product it can be concluded that the hydrogenation of cyclopentadiene dimer is thermodynamically controlled.

Note that although the energy value at the bottom of the results does not correspond to any particular thermodynamic property, a lower value still corresponds to a more thermodynamically stable compound as this energy is a sum of the distortions from the ideal.

{| class="wikitable" border="1"
|+ results from molecular mechanics for hydrogenation of cyclopentadiene dimer
! energy!! molecule 1 /Kcal.mol-1 !! molecule 2 /Kcal.mol-1 !! molecule 3 /Kcal.mol-1 !! molecule 4 /Kcal.mol-1
|-
| str || 1.2515 || 1.2861 || 1.132 || 1.268
|-
| ben || 20.8585 || 20.6031 || 13.0418 || 19.1509
|-
| str ben || -0.8393 || -0.8418 || -0.5659 || -0.8404
|-
| tor || 9.5146 || 7.6545 || 12.3966 || 11.0657
|-
| non 1-4 vdw || -1.5614 || -1.4326 || -1.3152 || -1.6202
|-
| 1-4vdw || 4.3327 || 4.2351 || 4.4256 || 5.7799
|-
| dip-dip || 0.4497 || 0.3773 || 0.141 || 0.1623
|-
| energy || 34.0063 || 31.8817 || 29.256 || 34.9661
|}

----

=== Stereochemistry of Nucleophilic Addition to a pyridinium ring (NAD+ analogue) ===

[[Image:JLORGWIKNADmols.jpg|thumb|500px| ]]

Two examples of stereochemistry of nucleophilic addition to a pyridinium ring were investigated: 5 being converted into 6 using MeMgI and 7 being converted to 8 upon reaction with PhNH2.

If the MeMgI component is put into the calculation an error message is observed stating that ‘WARNING! No atom type was assigned to the selected atom!’ with the selected atom being the Mg. This is because the MM2 method is unable to perform calculations with metals.

When a molecule of the Grignard reagent MeMgI comes close to molecule 5, the Mg is able to coordinate with the oxygen of the amide<ref>A. G. Schultz, L. Flood and J. P. Springer, The Journal of Organic Chemistry, 2002, 51, 838-841. DOI: 10.1021/jo00356a016</ref>. This results in strong region and stereo control as the δ- Me group is forced to attack the 4 position of the pyridinium ring rather than any other position of the ring.
{|
| [[Image:JLORGWIKNAD2.jpg|thumb|300px|Grignard reagent coordinating with amide of molecule 5 ]]
|}
According to the literature there are 2 possible conformations of 5: where the oxygen of the amide is above the plane of the pyridinium ring or simply in the plane. However the computational analysis only revealed the conformation where the oxygen was above the plane of the ring (slightly) after trying many different conformations before optimising the geometry. It was not found to be possible to find a conformational minima with the carbonyl below the plane of the ring. Therefore when the Mg coordinates the methyl group has to add above the plane of the ring resulting in the conformation of molecule 6.

{|
| [[Image:JLORGWIKNAD3.jpg|thumb|400px|the conformation of molecule 5 ]]
|}

Molecule 8 is formed into the given conformation due to dipolar coupling, as shown in the image below, between the H shown and the phenyl group<ref>S. Leleu, C. Papamicaël, F. Marsais, G. Dupas and V. Levacher, Tetrahedron: Asymmetry, 2004, 15, 3919-3928. DOI:10.1016/j.tetasy.2004.11.004.</ref> This attraction is seemingly strong enough to cause the incoming amine nucleophile to form into this conformation.
{|
| [[Image:JLORGWIK8coord.jpg|thumb|300px|Coordination causing the confomation of molecule 8 ]]
|
[[Image:JLORGWIK8conform.jpg|thumb|500px|Coordination causing the conformation of molecule 8 shown with green line ]]
|}

The analysis of this reaction did not take into account any MO effects at all meaning that potential stabilising or destabilising effects have been ignored. This said the method does explain the observed conformations reported in the literature, but if MO effects had been taken into account a more complete explanation may be made.

'''References'''
<references/>

=== Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol. ===

[[Image:JLORGWIKtaxol.jpg|thumb|450px|Molecules 10 and 11]]

When either molecule 10 or 11 as I had initially drawn them were put through the minimising energy calculation of MM2 the molecule changed to the form shown in 11 with the carbonyl pointing down in respect to the page. Upon manual manipulation in ChemBio3D of the position of the carbonyl group the desired geometry of molecule 10 was achieved, immediately it was noted that it possessed a higher final energy (59.7897 kcal/mol) compared to 44.3248 kcal/mol for molecule 11, with this greater degree of stability in 11 being due largely to a difference in the bending energy. This means that to have the carbonyl group pointing up destabilises the molecule by forcing the molecule to be more bent.

A hyper-stable alkene is a compound where an alkene which is part of a cyclic system serves to reduce the overall strain energy of the compound.<ref> 1. P. Camps, X. Pujol, S. Vázquez, M. A. Pericàs, C. Puigjaner and L. Solà, Tetrahedron, 2001, 57, 8511-8520. DOI:10.1016/S0040-4020(01)00802-X</ref> Ordinarily having an alkene in a ring increases the strain energy of the compound but in a hyperstable alkene the strain energy is lowered which can be demonstrated using the heats of hydrogenation.<ref> 1. D. P. G. Hamon and G. Y. Krippner, The Journal of Organic Chemistry, 2002, 57, 7109-7114. DOI:10.1021/jo00052a024</ref>

As such, if the molecule undergoes a functional group conversion at the alkene it can be expected to proceed slowly as the alkene being in the ring has effectively stabilised the molecule making a conversion likely to be thermodynamically unfavourable.

'''References'''

<references/>

----

== Modelling using Semi-Empirical Molecular Orbital theory ==

=== Regioselective Addition of dichlorocarbene ===
{|
| [[Image:JLORGWIKdi1.jpg|thumb|200px|Molecules 12 and its hydrogenated version 12H]]
| [[Image:JLORGWIKdi2.jpg|thumb|200px|HOMO ]]
| [[Image:JLORGWIKdi3.jpg|thumb|200px|HOMO-1 ]]
|}

{|
| [[Image:JLORGWIKdi4.jpg|thumb|200px|LUMO ]]
| [[Image:JLORGWIKdi5.jpg|thumb|200px|LUMO+1 ]]
| [[Image:JLORGWIKdi6.jpg|thumb|200px|LUMO+2 ]]
|}
The HOMO shows that the Cl-Cσ* orbital lies anti peri-planar to the exo π orbital which is occupied. This provides a stabilising effect for the exo double bond which in turn makes the endo alkene more nucleophilic in an electrostatic sense and a frontier orbital sense. <ref> B. Halton, R. Boese, H. Rzepa, J. Chem. Soc., Perkin Trans. 2, 1992, 447 - 448, DOI: 10.1039/P29920000447 </ref>

Both molecules 12 and 12H were subjected to optimisation and frequency calculation using B3LYP/6-31G(d,p) submitted through SCAN. The resulting .fchk files were put into Gaussview 3.0 and their vibrational frequencies inspected.
{|
| [[Image:JLORGWIKdi7.jpg|thumb|500px|IR spectrum of molecule 12 ]]
|}
The observed frequency of the C=C double bonds stretches in 12 are observed at 3176cm-1 and 3178cm-1. The C-Cl stretch is observed at 770.8cm-1.

{|
| [[Image:JLORGWIKdi8.jpg|thumb|200px|vibration 770.8 ]]
| [[Image:JLORGWIKdi9.jpg|thumb|200px|vibration at 3176 ]]
| [[Image:JLORGWIKdi10.jpg|thumb|200px|vibration at 3178 ]]
|}
In the hydrogenated version of 12 with only 1 double bond, labelled 12H, the C=C double bond stretch is observed at 1736cm-1 and the C-Cl stretch is observed at 551cm-1

{|
| [[Image:JLORGWIKdi11.jpg|thumb|200px|vibration at 551 ]]
| [[Image:JLORGWIKdi12.jpg|thumb|200px|vibration at 1736 ]]
|}

The absence of the 2nd double bond in 12H has had some profound effects on the observed stretching frequencies. Firstly the C=C stretching frequencies in 12 are at much higher wave numbers (3176,3178cm-1) compared to 12H (1736cm-1). Ordinarily stretching for C=C double bonds at values around 3170cm-1 indicates a conjugated system whereas 1736 would be an isolated double bond. The system is not conjugated so this must be explained through the presence of the chlorine syn to the double bond providing stability via the anti periplanar interactions of the Cl-Cσ* orbital and the exo π orbital.

The C-Cl stretch is also observed at a lower wavenumber in 12H than in 12. Which is a result of the presence of the extra C=C double bond.

'''References'''

<references/>

----

== Mini Project- Stereoselective dissolving metal reduction ==

A recent paper <ref>1. L. Castellanos, C. Duque, J. Rodríguez and C. Jiménez, Tetrahedron, 2007, 63, 1544-1552.</ref> described the reduction of the carbonyl of molecule 13 into the alcohol of 14 with complete stereoselectivity. In the following project I will discuss how it could be determined that the reaction had come to completion, how the stereoisomerism could be determined, why the particular stereoisomer was created, whether the 13C NMR and related 3JH-H couplings match those stated in the literature and whether the optical rotation matches that given in the literature.
{|
| [[Image:JLORGWIK13and14.jpg|thumb|550px|Molecules 13 and 14 ]]
|}
=== Reaction Completion ===

The reaction converting 13 into 14 requires the reduction of the ketone in 13 into the alcohol of 14 using the mechanism of dissolved metals (Li in NH3 in this case) to reduce the functional group. A very high yield of 92% is recorded in the paper.

The reaction can be said to be complete when the IR spectrum shows no signs of a carbonyl band which would indicate the presence of molecule 13. An IR stretch for an alcohol group would also show the presence of 14, but if there is still a carbonyl stretch then it would not answer whether the reaction had gone to completion. NMR might also be used to indicate the presence of the protons not present in 13 (the alcohol and the proton on the carbon of the alcohol). Though again these would merely show the existence of 14, not prove the reaction had gone to completion.

Therefore to determine whether the reaction has gone to completion the IR spectrum would be investigated. The paper does not give the experimental IR spectra, so instead the peaks of interest will be discussed using the computational spectra to illustrate how the end point of the reaction could reliably be concluded.
{|
| [[Image:JLORGWIK13IR.jpg|thumb|700px|IR spectra of 13 and 14]]
|}
As would be expected the analysis shows that for molecule 13 there is a significant peak of intensity at 1806cm-1 corresponding to a stretching vibration in the carbonyl group. This is not present in the IR of molecule 14, so an absence of this in the spectra of the product that has been synthesised would indicate the reaction has gone to completion.

=== Determining and Predicting the Stereochemistry ===

Molecule 14 is potentially 1 of 2 optical isomers, though only 1 is created in the synthesis laid out in the literature. The 2 possible enantiomers are shown below as 14 and 14* where 14 is the product said to be formed in the synthesis.
{|
| [[Image:JLORGWIK14and14H.jpg|thumb|550px|Enantiomers 14 and 14* ]]
|}
Isomer 14 is the R enantiomer whilst 14* is the S enantiomer following from the CIP system<ref> 1. L. Castellanos, C. Duque, J. Rodríguez and C. Jiménez, Tetrahedron, 2007, 63, 1544-1552.</ref> . As such enantiomer 14 will bend polarised light to the right and 14* would bend polarised light to the left allowing the exact conformation to be deduced. This information was gathered experimentally and presented in the literature and the value of -11.6 for [α]D20 thus confirming that the molecule is in the form shown in molecule 14.

The optical rotation was calculated returning an answer of 174.44˚ for molecule 14, which can be converted to -5.56˚ though this is still far from the experimental value. However as the job took 1 day 3 hours 38 minutes 2.7 seconds of CPU time I concluded that it was not worth ‘playing’ with the configuration of the molecule to get a closer match as it suggests in the script. This would merely tie up the queue and waste the computers, others in the queue and my time.

Similarly the result of [α]D20 for molecule 13 was -19.5˚ in the literature and 169.26˚ (-10.74˚) from the calculation. Again the result was far off but with a CPU time of 23 hours 13 minutes 6.1 seconds the same conclusion was reached with regards to repeating with a different conformation.

However the fact remains that the way in which the stereochemistry can be confirmed is through investigation of the optical rotational properties of the molecule. The experimental result from the literature confirms the molecule is as shown in 14. It can also be concluded that using a computational analysis for predicting optical rotation is not yet at a stage where the accuracy is high nor where the calculation is quick.

The synthesis proceeds with complete control of stereochemistry making an investigation into why such control is achieved worthwhile.

It can be seen upon a glance inspection that the OH group in the position shown in 14 might provide less steric hindrance than in 14* as there is a methyl group on the adjacent carbon to the alcohol which is in the same direction, and by minimising the steric hindrance here the energy of the system will be lowered.

This would be shown quantitatively in the IR output file where the sum of electric and thermal energies is given. The energy is in Hartrees allowing for an easy comparison of the free energies of the molecules: -662.159136 for 14 and -662.158468 for 14*. Which being extremely similar means the answer must not lie with 1 molecule being inherently lower in energy.

Running the MM2 geometry optimisation on molecules 14 and 14* and comparing the energy values also shows that 14 is going to be the ever so slightly favourable molecule. 14 exhibits less variation from the ideal in bending (3.65 to 3.85Kcal.mol-1) and torsion (10.91 to 11.15Kcal.mol-1).

However these differences are really quite small, meaning that the vast favourability of 14 over 14* is unlikely to be purely thermodynamically controlled meaning that the reaction must be somewhat kinetically controlled with the answer lying in the mechanism.

The reaction proceeds as follows<ref>1. G. Stork and S. D. Darling, Journal of the American Chemical Society, 2002, 86, 1761-1768</ref>:
{|
| [[Image:JLORGWIKmpmech.jpg|thumb|800px|Mechanism for the reduction of 13 to 14 ]]
|}
The addition of the H+ to the ketyl ,<ref>Some modern methods of organic synthesis, W. Carruthers, pg 443, 1986</ref> <ref>IUPAC</ref> occurs through axial protonation of the ketyl. The axis on which the protonation is determined by the best overlap between the incoming H+ ions orbital and the ketyl LUMO orbital. If the attack is made from ‘above’ the ring as drawn this overlap is less obstructed as shown in the diagram below of the ketyl LUMO.
{|
| [[Image:JLORGWIKKETYL.jpg|thumb|500px|The LUMO of the ketyl, the radical carbon is highlighted ]]
|}
=== Comparison of 13C NMR from literature and computational analysis ===

13C NMR spectra were calculated for molecules 13 and 14 using the molecules which had been optimised for their geometry at the mpw1pw91/6-31(d,p) by creating a Gaussian input files altered to perform NMR calculations. These were submitted to the SCAN and the data then analysed in Gaussview 3.0. The purpose was to determine whether the structures put forth in the literature match those predicted analytically by comparison of the NMR spectra.

The literature reports the 13C NMR of compound 13 as: 13C NMR (125 MHz, CDCl3) δ (ppm): 213.25 (C-3, s), 146.28 (C-11, s), 111.06 (C-13, t), 45.66 (C-5, d), 45.24 (C-4, d), 41.74 (C-1, t), 38.32 (C-7, d), 38.20 (C-2, t), 36.32 (C-9, t), 33.99 (C-10, s), 27.54 (C-6, t), 23.02 (C-8, t), 22.71 (C-12, q), 16.10 (C-15, q), 11.18 (C-14, q). The computationally predicted spectra <ref>Predicted NMR of molecule 13 DOI:10042/to-2530</ref> is:13C NMR (CDCl3) δ (ppm): 207.82 (C-2), 147.02 (C-12), 109.80 (C-14), 47.85 (C-3), 45.55 (C-4), 43.2 (C-6), 41.58 (C-8), 38.99 (C-1), 38.38 (C-10), 33.22 (C-5), 31.90 (C-7), 26.03 (C-9), 23.32 (C-13), 18.61 (C-15), 13.69 (C-11).

The computational analysis supplies no data on the coupling of the carbon nuclei so no singlet, doublet etc assignments can be made. The paper has labelled the carbons in a different manner to how Gaussview has them, and as such to compare the data it was necessary to decipher the common carbons. This was done by putting the NMR chemical shift values along with their carbon number into a table in Excel. The data was then sorted such that the chemical shift values were put into a descending order whilst keeping the carbon label. This allowed for the data from the reference and from the computational analysis to be seen side by side.

The data matched very well with an average difference between the reference and calculated chemical shifts of just 2.09ppm; the average being calculated by summing the modulus of the differences and dividing by the number of carbons. It can thus be concluded that the data reported in the literature and the values calculated give good agreement on the structure of compound 13 though the labelling is different in the reference.

[[Image:JLORGWIK13noH.jpg|thumb|450px|Molecule 13 with hydrogens removed for clarity ]]

{| class="wikitable" border="1"
|+ calculated and experimental NMR data for molecule 13
! Carbon # !! ref δ/ppm !! Carbon # !! calc δ/ppm
|-
| 11 || 147.11 || 12 || 147.43
|-
| 13 || 110.67 || 14 || 109.28
|-
| 3 || 76.86 || 2 || 74.26
|-
| 5 || 43.22 || 3 || 42.32
|-
| 1 || 39.93 || 4 || 41.726
|-
| 7 || 39.19 || 6 || 41.46
|-
| 4 || 38.88 || 4 || 41.22
|-
| 9 || 37.10 || 10 || 39.05
|-
| 10 || 33.78 || 5 || 33.50
|-
| 2 || 30.92 || 7 || 30.87
|-
| 6 || 26.05 || 1 || 30.60
|-
| 8 || 23.08 || 9 || 26.06
|-
| 15 || 16.68 || 15 || 18.76
|-
| 14 || 14.87 || 11 || 15.39
|}

The 13C NMR from the reference for molecule 14 is as follows: 13C NMR (125 MHz, CDCl3) δ (ppm): 147.11 (C-11, s), 110.67 (C-13, t), 76.86 (C-3, d), 43.22 (C-5, d), 39.93 (C-1, t), 39.19 (C-7, d), 38.88 (C-4, d), 37.10 (C-9, t), 33.78 (C-10, s), 30.92 (C-2, t), 26.05 (C-6, t), 23.08 (C-8, t), 22.82 (C-12, q), 16.68 (C-15, q), 14.87 (C-14, q). The computationally predicted spectra <ref>Predicted NMR spectrum of molecule 14 DOI:10042/to-2531</ref> is:13C NMR (CDCl3) δ (ppm): 147.43 (C-12), 109.28 (C-14), 74.26 (C-2), 42.32 (C-3), 41.73 (C-1), 41.46 (C-6), 41.22 (C-4), 39.05 (C-10), 33.50 (C-5), 30.87 (C-7), 30.61 (C-1), 26.06 (C-9), 24.14 (C-13), 18.76 (C-15), 15.39 (C-11).

Again the labelling was different between the reference and the computational analysis, so the same method was employed to allow for the correct comparisons to be made. This time the data was an even closer fit with a mean difference of just 1.69ppm between the 2 values. Once more it could be concluded that the structure reported in the paper is the same as that predicted using the computational analysis.

[[Image:JLORGWIK14noH.jpg|thumb|450px|molecule 14 with hydrogens removed for clarity ]]

{| class="wikitable" border="1"
|+ calculated and experimental NMR data for molecule 14
! Carbon # !! ref δ/ppm !! Carbon # !! calc δ/ppm
|-
| 3 || 213.25 || 2 || 207.82
|-
| 11 || 146.28 || 12 || 147.02
|-
| 13 || 111.06 || 14 || 109.80
|-
| 5 || 45.66 || 3 || 47.85
|-
| 4 || 45.24 || 4 || 45.55
|-
| 1 || 41.74 || 6 || 43.2
|-
| 7 || 37.32 || 8 || 41.58
|-
| 2 || 38.20 || 1 || 38.99
|-
| 9 || 36.32 || 10 || 38.38
|-
| 10 || 33.99 || 5 || 33.22
|-
| 6 || 27.54 || 7 || 31.90
|-
| 8 || 23.02 || 9 || 26.03
|-
| 12 || 22.71 || 13 || 23.32
|-
| 15 || 16.1 || 15 || 18.61
|}

''References''
<references/>

Rep:Mod:jlphyswik

2009-11-12T16:19:42Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. This is considerably longer than typical carbon-carbon bond lengths (sp3-sp3 1.54A, sp2-sp2 1.34A)<ref>Organic Chemistry, M.A. Fox, J.K. Whitesell, 2004, pg49, ISBN:0763721972</ref>. This might be expected as the transition structure is formed while the 2 molecules are some distance apart. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

Both new sigma bonds form simultaneously, as is necessary for a pericyclic reaction which by definition involve a concerted motion of electrons. This can be seen in the above diagram where the view of the vibration on the right clearly shows the ethene and the butadiene coming together in a fashion that would cause both bonds to form at the same time.

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T16:06:18Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (another angle)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T16:05:34Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction. The partly formed C-C sigma bonds were 2.21A. The lowest positive frequency vibration corresponded to a twisting rotation of both the butadiene and the ethene, with each turning the oppposite direction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T16:02:21Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants and products were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to having a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to optimise the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that the endo molecule is in a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T15:55:07Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

It can be seen that the HOMO of this transition state structure is 's' symmetrical with respect to the plane used before. This mirror plane runs through the middle of the ethene double bond, then through the middle of the bond between the 2 central carbons in the butadiene part. The HOMO of the transition state is the MO involved in the reaction, and by being 's' symmetrical allows for the reaction to proceed, serving as further proof that this is the correct transition structure.

In conclusion of this section, for a pericyclic reaction, such as a Diels Alder reaction, to proceed, molecular orbital symmetry must be conserved. This is shown in this example by the HOMO of butadiene, the LUMO of ethen and the HOMO of the transition state all being 's' symmetric. The HOMO of the product of the reaction is also 's' symmetric.

{|
| [[Image:jlphysbutaprodHOMO.jpg|400px|thumb|HOMO of the product clearly has 's' symmetry]]
|}

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

File:JlphysbutaprodHOMO.jpg

2009-11-12T15:54:56Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T15:40:27Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best accuracy to time results; at least for molecules as simple as are dealt with here. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T15:38:05Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || The LUMO has 's' symmetry with respect to the plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T15:37:40Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlphysbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || comment on symmetry with plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T15:37:11Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:Jlphys27.jpg|300px]] || [[Image:jlbutaHOMO.jpg|300px]] || [[Image:JlphysbutaLUMO.jpg|300px]]
|-
| || It can be seen that the HOMO has 'a' symmetry with respect to the plane || comment on symmetry with plane
|}

For a pericyclic reaction the symmetry of the orbitals must be conserved. In the reaction the LUMO of butadiene is used, with electron density from the π bond of the ethene (the HOMO of ethene) donating into the butadiene's LUMO π*, breaking the double bonds in butadiene and forming 2 new sigma bonds. The π orbital of the ethene is obviously going to be symmetric with respect to the plane, and as such this reaction is allowed.

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

File:JlphysbutaLUMO.jpg

2009-11-12T15:31:25Z

Jl807:

File:JlphysbutaHOMO.jpg

2009-11-12T15:29:29Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T12:57:03Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==
{|
| [[Image:jlphysdanorm.jpg|thumb|500px]]
|}

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

File:Jlphysdanorm.jpg

2009-11-12T12:57:01Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T12:52:27Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T12:51:55Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of atoms. The products, and eventually the transition states, can be compared though due to both having the same number (and type) of atoms. While trying to construct the endo molecule (4) it kept minimising to the exo molecule(3) which was a further indication that it was a higher energy state. Eventually molecule 4 was constructed by taking the molecule of 3 and swapping the hydrogens with the furan ring rather than trying to draw it from scratch.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation at the HF,3-21g level, using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny).

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme)]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T12:43:21Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme.jpg|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of, the products, and eventually the transition states, can be compared though due to the same number of atoms being in place. Molecule 4 kept optimising to molecule 3, clearly indicating it was a higher energy state.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny)

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T12:43:04Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

In this section the regioselectivity of the Diels Alder reaction was investigated using the following reaction between maleic anhydrude and cyclohexa-1,3-diene as an example:

{|
| [[Image:jlphysdastereoscheme|thumb|500px|reaction scheme to be invesitgated]]
|}

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of, the products, and eventually the transition states, can be compared though due to the same number of atoms being in place. Molecule 4 kept optimising to molecule 3, clearly indicating it was a higher energy state.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny)

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

File:Jlphysdastereoscheme.jpg

2009-11-12T12:42:20Z

Jl807:

Rep:Mod:jlphyswik

2009-11-12T12:27:36Z

Jl807: /* Reaction of Butadiene with ethene */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]
|}

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of, the products, and eventually the transition states, can be compared though due to the same number of atoms being in place. Molecule 4 kept optimising to molecule 3, clearly indicating it was a higher energy state.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny)

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T12:23:42Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of, the products, and eventually the transition states, can be compared though due to the same number of atoms being in place. Molecule 4 kept optimising to molecule 3, clearly indicating it was a higher energy state.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny)

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|600px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|290px]] || [[Image:jlphys50.jpg|290px]] || [[Image:jlphys51.jpg|290px]] || [[Image:jlphys52.jpg|290px]]
|-
| LUMO || [[Image:jlphys53.jpg|290px]] || [[Image:jlphys54.jpg|290px]] || [[Image:jlphys55.jpg|290px]] || [[Image:jlphys56.jpg|290px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.

Rep:Mod:jlphyswik

2009-11-12T12:22:17Z

Jl807: /* The regioselectivity of the Diels Alder reaction */

This is James Lees' physical component for 3rd year computational lab

= Tutorial on the Cope Rearrangement =
In this section I investigate the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem. The goals are to find the low energy minima and transition state structures using the potential energy surface of C6H10, a comparison of which should allow the determination of the preferred mechanism.To investigate the reaction the reactants/products were optimised allowing for the energy of the 1,5-hexadiene to be found and then contrasted with the energies from the optimised transition structures. This would allow for a determination of which transition structure is more likely to be involved, thus determining which pathway is kinetically favoured.

The reaction is a [3,3] sigmatropic shift rearrangement, a pericyclic reaction, which is thought to proceed through a boat or a chair transition state, this will be investigated at the B3LYP/6-31G level.

[[Image:jlphyscopescheme.jpg|500px]]

== Optimising the Reactants and Products ==

First a molecule of 1,5-hexadiene was drawn in gaussview. This was then arranged such that the carbons were arranged to make the carbon carbon linkages in an anti conformation as shown. This was then optimised at the HF, 3-21G level.

{|
| [[Image:jlphys1.jpg|thumb|300px|anti linkage pre optimisation ]]
| [[Image:jlphys2.jpg|thumb|300px|anti linkage post optimisation]]
|}

This molecule belonged to the Ci point group and had an overall energy of -231.6925a.u. This meant that it was the same molecule as 'anti 2' from appendix 1.

Next a molecule of 1,5-hexadiene was drawn and arranged to give it gauche linkage. Again this was then optimised to the HF,3-21g level.

{|
| [[Image:jlphys3.jpg|thumb|300px|gauche linkage pre optimisation]]
| [[Image:jlphys4.jpg|thumb|300px|gauche linkage post optimisation]]
|}

This molecule belonged to the C2 point group and had an overall energy of -231.6917a.u. This meant this molecule corresponded to 'gauche 4' from appendix 1.

The script indicated that the Ci conformer would be the lowest energy possible which had been my initial prediction when drawing that conformer. This is because this conformation both minimises steric interactions and allows favourable overlap of σ* C-H orbitals with adjacent σ C-H orbitals as shown in the diagram (note only 1 interaction is shown for clarity but more exist, these interactions are maximised in 'anti 2')

{|
| [[Image:jlphys5.jpg|thumb|400px|diagram showing anti linkage MO interactions]]
|}

The 'anti 2' conformer was then optimised using DFT, B3LYP 6-31g. A comparison between this structure and the HF 3-21g structure showed the bond lengths were all the same to 2d.p on the angstom scale, though some bonds were different in length at scales below this, these values are outside of the reasonable margin of error for bong lengths of ~.1A.

Next a frequency calculation was performed on the B3LYP 6-31g structure. This confirmed that the structure was a minimum by returning no negative frequencies for any vibrations. The IR spectrum of the compound is shown below along with the table of vibrations to confirm no negative frequencies were observed.
{|
| [[Image:jlphys6.jpg|800px|IR spectrum and lowest vibrational frequencies.]]
|}

The following thermodynamic data was recorded:

This molecule is an asymmetric top.

Rotational symmetry number 1.

Rotational temperatures (Kelvin) 0.77951 0.06368 0.06269

Rotational constants (GHZ): 16.24234 1.32678 1.30635

Zero-point vibrational energy 376724.9 (Joules/Mol)

90.03941 (Kcal/Mol)

== Optimising the Transition Structures ==
The chair and boat transition structures were now invesitgated using a variety of methods. I then performed an IRC calculation on each to demonstrate they truely were a transition state in the cope rearrangement. Finally, the relative energies of the transition states and the product were compared to allow for a determination of which reaction pathway is preferred, and this is is then discussed.

=== Computing Force Constants at the beginning ===

First an allyl fragment was drawn in gaussview and then optimised using HF, 3-31g. Two of these fragments were now arranged in a single mol group approximately 2.2A apart and in a shape that looked chair like. The chair transition state belongs to the C2h point group. An opt+freq calculation was performed on this molecule, optimising it to a TS(Berny) and at the 3-21g level. This returned a structure corresponding to the chair transition state. It was confirmed to be a transition state by analysis of the vibrational results which showed a single imaginary frequency at -818cm^-1. This vibration clearly corresponded to the cope rearrangement.

{|
| [[Image:jlphys7.jpg|thumb|300px|An optimised allyl fragment]]
| [[Image:jlphys8.jpg|thumb|300px|Optimised chair transition structure]]
|-
| [[Image:jlphys9.jpg|thumb|300px|Cope rearrangement vibration]]
| [[Image:jlphys10.jpg|thumb|300px|Cope rearrangement vibration]]
|}

=== Using the Redundant Coordinator ===

Taking the initial guess at the transition structure from the 2 allyl fragments arranged into roughly a chair conformation, I now proceeded to find the transition structure using the redundant coordinate method. The first step was to freeze the 'bonds' between the 2 fragments. This was then minimised to a minimum. I then took this and changed the redundant coordinate editor options from freeze on the bonds to derivative. This was again minimised. The purpose of this sequence is that everything other than the interfragment geometry is optimised, then the interfragment geometry is minimised.

{|
| [[Image:jlphys11.jpg|thumb|300px|optimised transitiion structure]]
|}

The bond lengths between the fragments were 2.02A.

=== QST2 and QST3 ===

In this section I investigated the QST2 and QST3 methods for finding transition structures.

First 2 molecules of 1,5-hexadiene were drawn such that they would be the 2 different forms following from the cope rearrangement. Care was taken to ensure the labelling of the carbons was consistant between the 2 molecules.
{|
|[[Image:jlphys12.jpg|thumb|400px| Before and after a cope rearrangement ]]
|}

These molecules were used as the inputs for a QST2 opt+freq calculation. This job failed with the returning proposed transition structure being of the following form:

{|
| [[Image:jlphys13.jpg|thumb|400px|Failed transition structure]]
|}

To correct this the 2 input molecules had their dihedral angles, and internal bond agles altered as in the script. The 2 input molecules now looked like:
{|
| [[Image:jlphys14.jpg|thumb|400px|altered inputs for QST calculation]]
|}

These were then used as the input for the QST2 calculation again. This time the calculation would not run. The returning error said 'Try using 3 structures as input for QST transition state search'. Therefore I decided to draw what I assumed the transition structure should look like and perform a QST3 calculation. Again care was taken to ensure consistant labelling between carbon atoms.

{|
| [[Image:jlphys15.jpg|thumb|400px|guessed transition structure]]
|}

This calcualtion was successfully completed, an imaginary vibration was observed at -839cm^-1 corresponding to the cope rearrangement via a boat transition state.
{|
| [[Image:jlphys16.jpg|thumb|400px|output transition structure]]
|-
| [[Image:jlphys17.jpg|thumb|300px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys18.jpg|thumb|300px|Imaginary vibration (other extreme)]]
|}

=== IRC ===

An IRC calculation was performed on the chair TS found from the first method, and on the boat TS found from the QST3 calculation. Both clearly showed that they were undergoing a cope rearrangement, but neither had reached a point which could be concluded to be a minimum, and certainly the Ci (anti2) molecule was not the end point for either calculation. Of the 3 options given at the end of the scripts section on IRC, I decided that computing the force constants at every step would be the best choice for finding which conformation they ended up in. This is because it should give the best result, and for a reasonably small molecule such as 1,5-hexadiene it shouldn't be massively time consuming. To save more time both jobs were submitted to SCAN.

{| class="wikitable" border="1"
|+ Molecules from initial IRC calculation
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys19.jpg|300px]] || [[Image:jlphys20.jpg|300px]]
|-
| End || [[Image:jlphys21.jpg|300px]] || [[Image:jlphys22.jpg|300px]]
|}

{| class="wikitable" border="1"
|+ Molecules from IRC calculation where force constants are constantly calculated
! Stage !! boat TS !! chair TS
|-
| Beginning || [[Image:jlphys23.jpg|300px]] || [[Image:jlphys24.jpg|300px]]
|-
| End || [[Image:jlphys25.jpg|300px]] || [[Image:jlphys26.jpg|300px]]
|}

It can be seen that after this kind of calculation the final geometry is much more easily observed. Whichever transition state pathway is followed, the optimal conformer for the end point is still anti2.

=== Activation Energies ===

The transition structures were now optimised to the DFT, B3LYP 6-31g level. A table showing comparisons between the transition structures and the product, hexadiene, is shown below.

{| class="wikitable" border="1"
|+
! Property !! Boat !! Chair TS !! 1,5-hexadiene
|-
| Energy/a.u. || -234.4928 || -234.5055 || -234.5597
|-
| Fragment seperation/A || 2.25 || 2.03 || N/A
|-
| C-C bond length/A || 1.39 || 1.41 || 1.55
|-
| C-C-C bond angle/degrees || 122.9 || 120.9 || N/A
|}

Making the activation energy for conversion through the boat transition state =0.0669a.u. or 165kJ.mol-1, or 41.98kCal.mol-1. The conversion through the chair transition state =0.0542a.u. or 142.30KJ.mol-1 or 34.01Kcal.mol-1. This matches fairly well to the literature values given in the script.

{| class="wikitable" border="1"
|+ Activation Energies comparison between literature and calculated values/Kcal.mol-1
! Calculated chair pathway !! literature chair pathway !! calculated boat pathway !! literature boat pathway
|-
| 34.01 || 33.5 || 41.98 || 44.7
|}

The calculated value is closer for the chair form, though both are reasonably close, in fact the calculated value for the chair is within the margin of error for the literature value. Certainly the right order is observed between the 2 with the chair form requiring less energy than the boat form. WHY?

= The Diels Alder Cycloaddition =

In this section the Diels Alder reaction is studied as an example of comparing reaction pathways. The contribution of molecular orbitals to the reaction mechanism is looked at, and the reason for the high level of regioselectivity found in DA reactions is also investigated.

== Reaction of Butadiene with ethene ==

Cis-butadiene was constructed in gaussview and the MOs were found using the AM1 method.

{| class="wikitable" border="1"
|+ Cis-butadiene and its Frontier Orbitals
! Cis-butadiene !! HOMO !! LUMO
|-
| [[Image:jlphys27.jpg|300px]] || [[Image:jlphys28.jpg|300px]] || [[Image:jlphys29.jpg|300px]]
|-
| || comment on symmetry with plane || comment on symmetry with plane
|}

Next I looked to finding the transition state. The work on the tutorial section of the report had shown me that using the most simple method, calculating the force constants at the start of the reaction and minimising to a TS(Berny), provided the best results/time results. As such I drew what I believed should be the TS of the reaction.

{|
| [[Image:jlphys30.jpg|thumb|400px| First guess of the transition state]]
|}

This was then put into an opt+freq calculation, minimising to a TS Berny at HF 3-21g level. This returned the following molecule for the transition state.

{|
| [[Image:jlphys31.jpg|thumb|400px| TS optimised to TS(Berny)]]

This was the desired transition state structure, confirmed by the imaginary frequency found at -818cm^-1 which clearly corresponded to the DA reaction.

{|
| [[Image:jlphys32.jpg|thumb|400px|Imaginary vibration (1 extreme)]]
| [[Image:jlphys33.jpg|thumb|400px|Imaginary vibration (other extreme)]]
|}

The HOMO of the transition state structure is shown below

{|
| [[Image:jlphys34.jpg|thumb|400px|HOMO of the TS]]
|}

Then some analysis of this.

== The regioselectivity of the Diels Alder reaction ==

The reactants were first constructed in gaussview, then optimised to a HF 3-21g level.

{|
| [[Image:jlphys35.jpg|thumb|300px|Molecule 1]]
| [[Image:jlphys36.jpg|thumb|300px|Molecule 2]]
|-
| [[Image:jlphys37.jpg|thumb|300px|Molecule3]]
| [[Image:jlphys38.jpg|thumb|300px|Molecule4]]
|}

The relative energies of 3 and 4 are shown below, note these can’t be compared with the reagents due to there being a different number and type of, the products, and eventually the transition states, can be compared though due to the same number of atoms being in place. Molecule 4 kept optimising to molecule 3, clearly indicating it was a higher energy state.

{| class="wikitable" border="1"
|+ Energies of products/a.u.
! Molecule 3 !! Molecule 4
|-
| -605.7187a.u. ||-605.7213a.u.
|}

I first tried a Berny opt+freq calculation using the following guess for the transition state of molecule 4:

{|
| [[Image:jlphys39.jpg|thumb|400px|Initial guess for TS of 4]]
|}

Which failed. Several imaginary frequencies were observed, none of which were even close to the reaction coordinate. Knowing the transition state should be effectively aromatic I put in the aromatic bonds and set up the calculation again using opt+freq minimising to a TS(Berny)

As it seemed unlikely I would be able to get the transition state molecule near the real thing by chance, I decided to take the product molecules and edit the bonding so that the furan ring and the other section were not bonded, a distance was set of 2A. A berny calculation was set up. This was taking a long time so I stopped it and sent it to SCAN.

This came back entirely successful. Below the transition state structure starting from product 4 is shown, followed by the imaginary frequency at -643cm-1 corresponding to the reaction coordinate.
{|
| [[Image:jlphys40.jpg|thumb|400px|Molecule 4 TS ]]
|-
| [[Image:jlphys41.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
| [[Image:jlphys42.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

The energy of this transition state was -605.6104a.u. Below are the HOMO and LUMO.

{|
| [[Image:jlphys43.jpg|thumb|400px|HOMO ]]
|-
| [[Image:jlphys44.jpg|thumb|400px|LUMO ]]
|}

To find the transition state for molecule 3 I effectively mirrored the furan ring. The returning molecule had an imaginary frequency at -533.9cm-1, this being the reaction coordinate. The overall energy etc shown in table below. The imaginary frequency is shown below as well.

{|
|[[Image:jlphys45.jpg|thumb|400px|Molecule 3 TS ]]
|-
|[[Image:jlphys46.jpg|thumb|400px|Vibration corresponding to DA rxn ]]
|-
|[[Image:jlphys47.jpg|thumb|400px|Vibration corresponding to DA rxn (other extreme) ]]
|}

Below is a picture showing the 2 transition structures from the same orientation

{|
| [[Image:jlphys48.jpg|thumb|400px|Molecule 3 TS (left), Molecule 4 TS (left) ]]
|}

A table comparing properties of molecules and their transition states.

{| class="wikitable" border="1"
! !! Molecule 3 !! 3 TS !! Molecule 4 !! 4 TS
|-
| Energy/a.u. || 605.7187 || -605.9421 || -605.7213 (very similar to 3 showing the choice of product is kinetic) || -605.6104
|-
| Imaginary frequency/ cm^-1 || N/A || -533.9|| N/A || -643
|-
| HOMO || [[Image:jlphys49.jpg|300px]] || [[Image:jlphys50.jpg|300px]] || [[Image:jlphys51.jpg|300px]] || [[Image:jlphys52.jpg|300px]]
|-
| LUMO || [[Image:jlphys53.jpg|300px]] || [[Image:jlphys54.jpg|300px]] || [[Image:jlphys55.jpg|300px]] || [[Image:jlphys56.jpg|300px]]
|}

The difference in energy between the 2 products is only 1.6Kcal.mol-1. The difference in activation energies however through the 2 pathways is more notable. 140.1856kCal/mol for 3 and 69.59082kCal/mol for 4. Clearly then 4 is the more likely product kinetically.