File:MiniprojUV.jpg

2011-06-10T18:23:11Z

Ajm308:

Ajm3081

2011-06-10T18:22:41Z

Ajm308: /* IR Spectrum */

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

[[Image:Pt1orboverlapajm308.gif|thumb|upright|MO1]]

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:Stereochemrxn1ajm308.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face.

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:Stero2chemrxn1ajm308.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolisomersajm308.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:homo2.gif|thumb|upright|HOMO-2]]
| [[Image:homo1.gif|thumb|upright|HOMO-1]]
| [[Image:homo.gif|thumb|upright|HOMO]]
| [[Image:lumo.gif|thumb|upright|LUMO]]
| [[Image:lumo1.gif|thumb|upright|LUMO+1]]
| [[Image:lumo2.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:irdiene.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:irdihydro.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

=Structure Based Mini Project=

==Regio- and Stereo-selective conversion of Alkenes to Epoxides==

I will be investigating the stereo- and regio-selective conversion of alkenes to epoxides. The epoxidation of the 1,3-diene shown below yields either one of two products, also shown below. Molecular modelling will be used to obtain a variety of spectroscopic data for each potential epoxide product, which will then be compared to experimental date from the literature. Confirmation of the expected product is therefore possible using molecular modelling.

The epoxide formed during the epoxidation of the 1,3-diene is dependent upon the type of reagents used in the epoxidation. Epoxidation will usually take place stereoselectively on the least hindered face of the diene. If a bulky reagent is used,such as mCPBA, then the steric clash between the reagent and the dioxolane group leads to the reaction being forced on to the opposite face of the molecule. The epoxide and the dioxolane group are located on opposite faces of the molecule.

Direction of the reaction is possible, and cases where epoxidation on to the most hindered face have been reported in the literature. In the synthesis of the species with epoxide and dioxolane on the same face of the molecule, a hydroxyl group is added to the aromatic portion of the molecule. Hydrogen bonding is able to direct the epoxidation to the same face as the dioxolane group.

==Comparison of NMR Data provided by Guassian Calculation with that of Literature==

Calculated NMR Spectral data [13C & 1H] is included below. Experimental data is also shown.

'''13C NMR'''
[[Image:miniproj13Cnmr.jpg|center|NMR]]

13C Calculated NMR Data [ppm]: 26.8 (s), 28.3 (s), 48.6 (s), 49.8 (s), 74.3 (s), 75.0 (s), 110.6 (s), 127.4 (s), 144.9 (s).

13C Experimental NMR Data [ppm]<ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
25.2 (s), 27.1 (s), 50.2 (s), 54.5 (s), 73.9 (s), 76.8 (s), 108.7 (s), 125.5 (s), 130.0 (s).

The experimental data collected from literature for the 13C NMR is consistent with that produced by the gaussian calculation. The chemical shifts are very similar in each case and demostrate that this particular molecular mechanics method is a reliable way of predicting the NMR of an expected product.

Experimental NMR data is consistend with calculated NMR data indicating that the methodology used is an accurate and reliable way of predicting NMR shifts.

'''1H NMR'''

[[Image:miniproj1Hnmr.jpg|center|]]

Calculated 1H NMR Data [ppm]: 1.4 (s, 3H), 1.5 (s, 3H), 3.3 (dd, J = 5.0, 5.0 Hz), 3.6 (m, 1H), 4.3 (dd, J = 6.1, 2.8 Hz, 1H), 4.9 (dd, J = 6.7, 1.9 Hz), 6.6 (d, J = 5.0 Hz, 1H).

Experimental 1H NMR Data <ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
1.4 (s, 3H), 1.5 (s, 3H), 3.4 (dd, J = 4.5, 4.5
Hz, lH), 3.6 (m, lH), 4.5 (dd, J = 6.6, 2.4 Hz, lH), 4.7 (dd, J = 6.6, 1.8 Hz, lH), 6.7 (d, J = 4.5 Hz, 1H)

Again molecular modelling methodology has proved accurate in predicting shifts for 1H NMR. Using Jannochio, accurate 3J-J couplings values have also been found.

===IR Spectrum===
[[Image:miniprojIR.jpg|center|IR]]
{|
|'''IR Frequency/cm^-1'''
|'''Stretch/Bend'''
|----
|3094
|C-H Stretch Aromatic
|----
|2856
|C-H Alkane
|----
|1603
|C=C Stretch Aromatic
|----
|1267
|C-0
|----
|588
|C-Br
|----
|}

===UV/Vis Spectrum===
[[Image:UV_Vis(ep1).jpg|center]]

Max wavelength = 220.32nm

===Optical Rotation===

Optical rotation is the only possible way of deducing which enantiomer is present. Calculated optical rotations are -80.1 for the molecule with both groups on the same face, and +83.4 for the molecule with groups on opposite sides. This is expected as enantiomers by definition rotate plane polarised light in opposite directions to an equal extent.

File:MiniprojIR.jpg

2011-06-10T18:22:24Z

Ajm308:

File:Miniproj1Hnmr.jpg

2011-06-10T18:21:51Z

Ajm308:

Ajm3081

2011-06-10T18:21:33Z

Ajm308: /* Comparison of NMR Data provided by Guassian Calculation with that of Literature */

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

[[Image:Pt1orboverlapajm308.gif|thumb|upright|MO1]]

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:Stereochemrxn1ajm308.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face.

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:Stero2chemrxn1ajm308.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolisomersajm308.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:homo2.gif|thumb|upright|HOMO-2]]
| [[Image:homo1.gif|thumb|upright|HOMO-1]]
| [[Image:homo.gif|thumb|upright|HOMO]]
| [[Image:lumo.gif|thumb|upright|LUMO]]
| [[Image:lumo1.gif|thumb|upright|LUMO+1]]
| [[Image:lumo2.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:irdiene.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:irdihydro.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

=Structure Based Mini Project=

==Regio- and Stereo-selective conversion of Alkenes to Epoxides==

I will be investigating the stereo- and regio-selective conversion of alkenes to epoxides. The epoxidation of the 1,3-diene shown below yields either one of two products, also shown below. Molecular modelling will be used to obtain a variety of spectroscopic data for each potential epoxide product, which will then be compared to experimental date from the literature. Confirmation of the expected product is therefore possible using molecular modelling.

The epoxide formed during the epoxidation of the 1,3-diene is dependent upon the type of reagents used in the epoxidation. Epoxidation will usually take place stereoselectively on the least hindered face of the diene. If a bulky reagent is used,such as mCPBA, then the steric clash between the reagent and the dioxolane group leads to the reaction being forced on to the opposite face of the molecule. The epoxide and the dioxolane group are located on opposite faces of the molecule.

Direction of the reaction is possible, and cases where epoxidation on to the most hindered face have been reported in the literature. In the synthesis of the species with epoxide and dioxolane on the same face of the molecule, a hydroxyl group is added to the aromatic portion of the molecule. Hydrogen bonding is able to direct the epoxidation to the same face as the dioxolane group.

==Comparison of NMR Data provided by Guassian Calculation with that of Literature==

Calculated NMR Spectral data [13C & 1H] is included below. Experimental data is also shown.

'''13C NMR'''
[[Image:miniproj13Cnmr.jpg|center|NMR]]

13C Calculated NMR Data [ppm]: 26.8 (s), 28.3 (s), 48.6 (s), 49.8 (s), 74.3 (s), 75.0 (s), 110.6 (s), 127.4 (s), 144.9 (s).

13C Experimental NMR Data [ppm]<ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
25.2 (s), 27.1 (s), 50.2 (s), 54.5 (s), 73.9 (s), 76.8 (s), 108.7 (s), 125.5 (s), 130.0 (s).

The experimental data collected from literature for the 13C NMR is consistent with that produced by the gaussian calculation. The chemical shifts are very similar in each case and demostrate that this particular molecular mechanics method is a reliable way of predicting the NMR of an expected product.

Experimental NMR data is consistend with calculated NMR data indicating that the methodology used is an accurate and reliable way of predicting NMR shifts.

'''1H NMR'''

[[Image:miniproj1Hnmr.jpg|center|]]

Calculated 1H NMR Data [ppm]: 1.4 (s, 3H), 1.5 (s, 3H), 3.3 (dd, J = 5.0, 5.0 Hz), 3.6 (m, 1H), 4.3 (dd, J = 6.1, 2.8 Hz, 1H), 4.9 (dd, J = 6.7, 1.9 Hz), 6.6 (d, J = 5.0 Hz, 1H).

Experimental 1H NMR Data <ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
1.4 (s, 3H), 1.5 (s, 3H), 3.4 (dd, J = 4.5, 4.5
Hz, lH), 3.6 (m, lH), 4.5 (dd, J = 6.6, 2.4 Hz, lH), 4.7 (dd, J = 6.6, 1.8 Hz, lH), 6.7 (d, J = 4.5 Hz, 1H)

Again molecular modelling methodology has proved accurate in predicting shifts for 1H NMR. Using Jannochio, accurate 3J-J couplings values have also been found.

===IR Spectrum===
[[Image:IRep1.jpg|center|IR]]
{|
|'''IR Frequency/cm^-1'''
|'''Stretch/Bend'''
|----
|3094
|C-H Stretch Aromatic
|----
|2856
|C-H Alkane
|----
|1603
|C=C Stretch Aromatic
|----
|1267
|C-0
|----
|588
|C-Br
|----
|}

===UV/Vis Spectrum===
[[Image:UV_Vis(ep1).jpg|center]]

Max wavelength = 220.32nm

===Optical Rotation===

Optical rotation is the only possible way of deducing which enantiomer is present. Calculated optical rotations are -80.1 for the molecule with both groups on the same face, and +83.4 for the molecule with groups on opposite sides. This is expected as enantiomers by definition rotate plane polarised light in opposite directions to an equal extent.

File:Miniproj13Cnmr.jpg

2011-06-10T18:21:06Z

Ajm308:

Ajm3081

2011-06-10T18:20:44Z

Ajm308: /* Regio- and Stereo-selective conversion of Alkenes to Epoxides */

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

[[Image:Pt1orboverlapajm308.gif|thumb|upright|MO1]]

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:Stereochemrxn1ajm308.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face.

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:Stero2chemrxn1ajm308.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolisomersajm308.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:homo2.gif|thumb|upright|HOMO-2]]
| [[Image:homo1.gif|thumb|upright|HOMO-1]]
| [[Image:homo.gif|thumb|upright|HOMO]]
| [[Image:lumo.gif|thumb|upright|LUMO]]
| [[Image:lumo1.gif|thumb|upright|LUMO+1]]
| [[Image:lumo2.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:irdiene.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:irdihydro.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

=Structure Based Mini Project=

==Regio- and Stereo-selective conversion of Alkenes to Epoxides==

I will be investigating the stereo- and regio-selective conversion of alkenes to epoxides. The epoxidation of the 1,3-diene shown below yields either one of two products, also shown below. Molecular modelling will be used to obtain a variety of spectroscopic data for each potential epoxide product, which will then be compared to experimental date from the literature. Confirmation of the expected product is therefore possible using molecular modelling.

The epoxide formed during the epoxidation of the 1,3-diene is dependent upon the type of reagents used in the epoxidation. Epoxidation will usually take place stereoselectively on the least hindered face of the diene. If a bulky reagent is used,such as mCPBA, then the steric clash between the reagent and the dioxolane group leads to the reaction being forced on to the opposite face of the molecule. The epoxide and the dioxolane group are located on opposite faces of the molecule.

Direction of the reaction is possible, and cases where epoxidation on to the most hindered face have been reported in the literature. In the synthesis of the species with epoxide and dioxolane on the same face of the molecule, a hydroxyl group is added to the aromatic portion of the molecule. Hydrogen bonding is able to direct the epoxidation to the same face as the dioxolane group.

==Comparison of NMR Data provided by Guassian Calculation with that of Literature==

Calculated NMR Spectral data [13C & 1H] is included below. Experimental data is also shown.

'''13C NMR'''
[[Image:NMRep14.jpg|center|NMR]]

13C Calculated NMR Data [ppm]: 26.8 (s), 28.3 (s), 48.6 (s), 49.8 (s), 74.3 (s), 75.0 (s), 110.6 (s), 127.4 (s), 144.9 (s).

13C Experimental NMR Data [ppm]<ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
25.2 (s), 27.1 (s), 50.2 (s), 54.5 (s), 73.9 (s), 76.8 (s), 108.7 (s), 125.5 (s), 130.0 (s).

The experimental data collected from literature for the 13C NMR is consistent with that produced by the gaussian calculation. The chemical shifts are very similar in each case and demostrate that this particular molecular mechanics method is a reliable way of predicting the NMR of an expected product.

Experimental NMR data is consistend with calculated NMR data indicating that the methodology used is an accurate and reliable way of predicting NMR shifts.

'''1H NMR'''

[[Image:HNMRep14.jpg|center|]]

Calculated 1H NMR Data [ppm]: 1.4 (s, 3H), 1.5 (s, 3H), 3.3 (dd, J = 5.0, 5.0 Hz), 3.6 (m, 1H), 4.3 (dd, J = 6.1, 2.8 Hz, 1H), 4.9 (dd, J = 6.7, 1.9 Hz), 6.6 (d, J = 5.0 Hz, 1H).

Experimental 1H NMR Data <ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
1.4 (s, 3H), 1.5 (s, 3H), 3.4 (dd, J = 4.5, 4.5
Hz, lH), 3.6 (m, lH), 4.5 (dd, J = 6.6, 2.4 Hz, lH), 4.7 (dd, J = 6.6, 1.8 Hz, lH), 6.7 (d, J = 4.5 Hz, 1H)

Again molecular modelling methodology has proved accurate in predicting shifts for 1H NMR. Using Jannochio, accurate 3J-J couplings values have also been found.

===IR Spectrum===
[[Image:IRep1.jpg|center|IR]]
{|
|'''IR Frequency/cm^-1'''
|'''Stretch/Bend'''
|----
|3094
|C-H Stretch Aromatic
|----
|2856
|C-H Alkane
|----
|1603
|C=C Stretch Aromatic
|----
|1267
|C-0
|----
|588
|C-Br
|----
|}

===UV/Vis Spectrum===
[[Image:UV_Vis(ep1).jpg|center]]

Max wavelength = 220.32nm

===Optical Rotation===

Optical rotation is the only possible way of deducing which enantiomer is present. Calculated optical rotations are -80.1 for the molecule with both groups on the same face, and +83.4 for the molecule with groups on opposite sides. This is expected as enantiomers by definition rotate plane polarised light in opposite directions to an equal extent.

Ajm3081

2011-06-10T18:19:56Z

2011-06-10T13:24:10Z

Ajm308: /* Structure Based Mini Project */

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

'''DIAGRAM'''

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:5to6jsm108correct.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face. This is shown in the diagram below:

[[Image:NADfirstmecanismjsm108.gif|alt=Example alt text]]

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:7to8jsm108orrect.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

[[Image:7to8jsm10mechanism.gif|alt=Example alt text]]

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolsynjm108.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:HOMO-2joshmcicoll.gif|thumb|upright|HOMO-2]]
| [[Image:HOMO-1joshmcncoll.gif|thumb|upright|HOMO-1]]
| [[Image:homojoshmcncoll.gif|thumb|upright|HOMO]]
| [[Image:LUMOjoshmcicoll.gif|thumb|upright|LUMO]]
| [[Image:LUMO+1josmcnicoll.gif|thumb|upright|LUMO+1]]
| [[Image:LUMO+2johmcnicoll.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

[[Image:hydroprodjsm08t.gif|alt=Example alt text]]

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:product12irjsm18.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:hydroprodirjsm18.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

=Structure Based Mini Project=

==Regio- and Stereo-selective conversion of Alkenes to Epoxides==

I will be investigating the stereo- and regio-selective conversion of alkenes to epoxides. The epoxidation of the 1,3-diene shown below yields either one of two products, also shown below. Molecular modelling will be used to obtain a variety of spectroscopic data for each potential epoxide product, which will then be compared to experimental date from the literature. Confirmation of the expected product is therefore possible using molecular modelling.

[[Image:Epoxde.jpg|center|Reaction Scheme: Conversion of alkene to epoxide]]

The epoxide formed during the epoxidation of the 1,3-diene is dependent upon the type of reagents used in the epoxidation. Epoxidation will usually take place stereoselectively on the least hindered face of the diene. If a bulky reagent is used,such as mCPBA, then the steric clash between the reagent and the dioxolane group leads to the reaction being forced on to the opposite face of the molecule. The epoxide and the dioxolane group are located on opposite faces of the molecule.

Direction of the reaction is possible, and cases where epoxidation on to the most hindered face have been reported in the literature. In the synthesis of the species with epoxide and dioxolane on the same face of the molecule, a hydroxyl group is added to the aromatic portion of the molecule. Hydrogen bonding is able to direct the epoxidation to the same face as the dioxolane group.

{|
| [[Image:literaturreaction.jpg|thumb|upright|Reagents listed in Literature]]
| [[Image:epoxidatinmech.gif|thumb|upright|Epoxidation Mechanism:Backside Attack]]
|}

==Comparison of NMR Data provided by Guassian Calculation with that of Literature==

Calculated NMR Spectral data [13C & 1H] is included below. Experimental data is also shown.

'''13C NMR'''
[[Image:NMRep14.jpg|center|NMR]]

13C Calculated NMR Data [ppm]: 26.8 (s), 28.3 (s), 48.6 (s), 49.8 (s), 74.3 (s), 75.0 (s), 110.6 (s), 127.4 (s), 144.9 (s).

13C Experimental NMR Data [ppm]<ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
25.2 (s), 27.1 (s), 50.2 (s), 54.5 (s), 73.9 (s), 76.8 (s), 108.7 (s), 125.5 (s), 130.0 (s).

The experimental data collected from literature for the 13C NMR is consistent with that produced by the gaussian calculation. The chemical shifts are very similar in each case and demostrate that this particular molecular mechanics method is a reliable way of predicting the NMR of an expected product.

Experimental NMR data is consistend with calculated NMR data indicating that the methodology used is an accurate and reliable way of predicting NMR shifts.

'''1H NMR'''

[[Image:HNMRep14.jpg|center|]]

Calculated 1H NMR Data [ppm]: 1.4 (s, 3H), 1.5 (s, 3H), 3.3 (dd, J = 5.0, 5.0 Hz), 3.6 (m, 1H), 4.3 (dd, J = 6.1, 2.8 Hz, 1H), 4.9 (dd, J = 6.7, 1.9 Hz), 6.6 (d, J = 5.0 Hz, 1H).

Experimental 1H NMR Data <ref>Ba V. Nguyen, C. York, T. Hudlicky; "Chemoenzymatic Synthesis of Deoxyfluoroinositols," ''Tetrahedron'', Vol. 53, No. 26, pp. 8807-88141, '''1997'''.</ref>:
1.4 (s, 3H), 1.5 (s, 3H), 3.4 (dd, J = 4.5, 4.5
Hz, lH), 3.6 (m, lH), 4.5 (dd, J = 6.6, 2.4 Hz, lH), 4.7 (dd, J = 6.6, 1.8 Hz, lH), 6.7 (d, J = 4.5 Hz, 1H)

Again molecular modelling methodology has proved accurate in predicting shifts for 1H NMR. Using Jannochio, accurate 3J-J couplings values have also been found.

===IR Spectrum===
[[Image:IRep1.jpg|center|IR]]
{|
|'''IR Frequency/cm^-1'''
|'''Stretch/Bend'''
|----
|3094
|C-H Stretch Aromatic
|----
|2856
|C-H Alkane
|----
|1603
|C=C Stretch Aromatic
|----
|1267
|C-0
|----
|588
|C-Br
|----
|}

===UV/Vis Spectrum===
[[Image:UV_Vis(ep1).jpg|center]]

Max wavelength = 220.32nm

===Optical Rotation===

Optical rotation is the only possible way of deducing which enantiomer is present. Calculated optical rotations are -80.1 for the molecule with both groups on the same face, and +83.4 for the molecule with groups on opposite sides. This is expected as enantiomers by definition rotate plane polarised light in opposite directions to an equal extent.

Ajm3081

2011-06-10T12:52:12Z

Ajm308:

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

'''DIAGRAM'''

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:5to6jsm108correct.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face. This is shown in the diagram below:

[[Image:NADfirstmecanismjsm108.gif|alt=Example alt text]]

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:7to8jsm108orrect.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

[[Image:7to8jsm10mechanism.gif|alt=Example alt text]]

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolsynjm108.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:HOMO-2joshmcicoll.gif|thumb|upright|HOMO-2]]
| [[Image:HOMO-1joshmcncoll.gif|thumb|upright|HOMO-1]]
| [[Image:homojoshmcncoll.gif|thumb|upright|HOMO]]
| [[Image:LUMOjoshmcicoll.gif|thumb|upright|LUMO]]
| [[Image:LUMO+1josmcnicoll.gif|thumb|upright|LUMO+1]]
| [[Image:LUMO+2johmcnicoll.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

[[Image:hydroprodjsm08t.gif|alt=Example alt text]]

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:product12irjsm18.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:hydroprodirjsm18.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

=Structure Based Mini Project=

Ajm3081

2011-06-10T12:51:22Z

Ajm308: /* Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene */

=Introduction=

Computer modelling is becoming an ever more powerful and important tool in predicting the outcome of chemical reactions, including regioselectivity, stereoselectivity as well as the relative stability of major and minor products. The aim of this project is to gain a basic understanding of the techniques and applications of a range of computational methods

=Hydrogenation of the cyclopentadiene dimer=

==Cyclopentadiene dimerisation==

Cyclopentadiene reacts in a [4+2] cycloaddition reaction to yield as the major product the endo form. The selection of the endo form can either be attributed to thermodynamic or kinetic control.

Chem3D was used to model both the endo and the exo form and the MM2 force field was used for geometry optimisation. Total relative energies for the two possible products are shown below:

Exo Product: 31.88 kcal/mol
Endo Product: 34.01 kcal/mol

It can be deduced from looking at the above figures, that the reaction must indeed be under kinetic control. The endo product is less thermodynamically stable than the exo product so the reaction cannot be under thermodynamic control.

The kinetic control shown in this reaction, can be attributed to the more favourable orbital overlap situation in the endo configuration. This is shown in the diagram below:

'''DIAGRAM'''

==Hydrogenation of the cyclopentadiene dimer==

The favoured endo product in the initial dimerisation was then to have hydrogenation modelled. With two available double bonds which could undergo hydrogenation, there are again, two different products. The major product yielding from this reaction will either be under kinetic or thermodynamic control. The two possible products were modelled and then had geometry optimisation performed, again using the MM2 force field.

{| border="1"
|-
!
! Product 1
! Product 2
|-
! Stretching
| 1.28
| 1.09
|-
! Bending
| 19.80
| 14.52
|-
! Torsion
| 10.87
| 12.50
|-
! Van de Waals
| 5.64
| 4.51
|-
! Dipole/dipole
| 0.16
| 0.14
|-
! Energy (kcal/mol)
| 35.70
| 31.15
|}

The table shows valuable information obtained from the geometry optimisation calculation, showing the contributions to the total energy of the molecule, made from a number of other modes of energy. Product 2 has a lower total energy than Product 1, by 4.54 kcal/mol and is therefore the thermodynamic product of this reaction.

The largest contribution to the difference in energies between the two possible products comes from the torsional strain and the bending terms. Product 1 has higher values for both of these modes.

In product 2, the torsional strain is greater than in product 1. This indicates that it is preferable for the cyclopentadiene dimer to be hydrogenated as in the case of product 1 with respect to torsional strain. However, the higher bending contribution in product 3 outweighs the decrease in torsional strain and as such product 2 is preferred.

=Stereochemistry of nucleophillic addition to pyridinium ring (NAD+ analogues)=

==Reaction 1==

[[Image:5to6jsm108correct.gif|fram|alt=Example alt text|Reaction scheme showing the optically active derivative of prolinol reacting with methyl magnesium iodide to alkylate the pyridine ring in the 4-position]]

Once again, the initial step was to model the reactant and then use the MM2 force field method to perform geometry optimisation. A range of possible conformers were modelled and calculations were performed upon each. As expected, each conformer had different geometric characteristics and different thermochemical characteristics.

Dihedral angles were measured around the carbonyl functional group.

5 conformers were modelled, and created by repositioning of both the 5-membered ring and the ethereal oxygen. Due to the rigid nature of the aromatic portion and the carbonyl groups, no changes were made to this section of the molecule. Repositioning above, below and in plane with the aromatic portion led to 5 conformers. Results from the geometry optimisation are shown below:

{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
! Conformer 4
! Conformer 5
|-
! 5-membered Ring
| above plane
| above plane
| below plane
| below plane
| flat
|-
! Ethereal Oxygen
| above plane
| below plane
| above plane
| below plane
| flat
|-
! Energy of Molecule (kcal/mol)
| 44.41
| 44.62
| 44.70
| 43.11
| 43.13
|-
! Dihedral Angle
| 23.8
| 12.2
| 23.7
| 10.9
| 9.0
|}

The most stable conformer is the case where both the ethereal oxygen and the 5 membered ring are positioned below the planar aromatic portion of the molecule.

An optimum dihedral angle of 10.9 degrees was calculated, but the results also show that the carbonyl functional group is always located on the top face of the molecule. This constant location of the carbonyl group across all conformers gives rise the selective nature of methyl addition to the top face of the molecule. The grignard reagent used is able to coordinate the carbonyl oxygen on the top face of the molecule, and as such addition of the methyl group must occur on to the top face. This is shown in the diagram below:

[[Image:NADfirstmecanismjsm108.gif|alt=Example alt text]]

Limitations of the methodology used include the inability to factor in the grignard reagent when carrying out the calculations. This would be sure to make the calculations more representative of reality.

==Reaction of pyridinium ring with aniline==

[[Image:7to8jsm108orrect.gif|frame|alt=Example alt text|Reaction scheme showing the pyridinium ring reacting with aniline to form the product]]

The above scheme shows the reaction of aniline with pyridinium ring. Stereoselectivity is once again present in respect to the position of addition of the pyridinium ring.

In order to find the origin of this control, the reactant in the reaction was defined and the MM2 force field was used to optimise the geometry. Different conformers of the reactant were drawn and minimised using the MM2 force field, with the focus lying on the geometry of the carbonyl group. This gave different minimized geometries with different total energies and dihedral angles. Dihedral angles were measured using the carbonyl carbon and oxygen, along with the adjacent aromatic carbon, and the aromatic carbon adjacent to that one.

Once again, the reactant was modelled and the MM2 force field used to optimise geometry. Again, different possible conformers were modelled and optimised. Dihedral angles and total energy were measured.

The conformers were produced by repositioning of both the carbonyl group and the tertiary nitrogen group either above or below the plane of the molecule. Different permutations of these positions were modelled and data for each conformer are shown below:
{| border="1"
|-
! Property
! Conformer 1
! Conformer 2
! Conformer 3
|-
! Carbonyl Group
! Above plane
! Above plane
! Below plane
|-
! Tertiary Nitrogen Group
! Above plane
! Below plane
! Below plane
|-
! Energy (kcal/mol)
| 84.17
| 63.74
| 63.55
|-
! Dihedral Angle
| 22.6
| -16.8
| -18.1
|}

The lowest energy conformation has a dihedral angle of -18.1 degrees and has both the carbonyl group and the tertiary nitrogen group below the plane of the molecule.

Once again, the top face of the molecule is the site for addition. Attack occurs to the opposite face of the molecule from the carbonyl group in order to avoid any steric issues. As the most stable conformer has the carbonyl group on the bottom face of the molecule, the aniline is compelled to add to the top face.

[[Image:7to8jsm10mechanism.gif|alt=Example alt text]]

=Stereochemistry and reactivity of an intermediate in the synthesis of taxol=

Two isomers of an important intermediate in the production of Taxol are shown below:

[[Image:Taxolsynjm108.gif|alt=Example alt text]]

The type of isomerism present is atropisomerism. This occurs as a result of the impedence of rotation around a single covalent bond in a molecule. This impedence gives rise to stereoisomers.

Isomer A has the carbonyl group upwards, whereas isomer B has the carbonyl group downwards. The two isomers were modelled and geometries were optimised using the MM2 force field. The MMFF94 force field was also utilised in geometry optimisation. The table below shows the results:

{| border="1"
|-
! Molecule
! A
! B
|-
! MM2 Energy (kcal/mol)
| 55.32
| 49.43
|-
! Torsion (kcal/mol)
| 20.17
| 17.51
|-
! MMFF94 Energy (kcal/mol)
| 77.60
| 70.66
|}

Isomer B has a lower total energy than isomer A. Both of the methods used - force fields MM2 and MMFF94 - reach the same conclusion although the absolute energy levels are different. The energy difference between the two isomers is very similar in both cases.

=Modelling using semi-empirical MO theory: Regioselective addition of dichlorocarbene=

9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was modelled in ChemBio3D and then the geometry was optimised using the MM2 force field to yield a total energy of 17.90 kcal/mol.

The MOPAC/RM1 method was then utilised in order to produce an approximation of the valence electron molecular orbitals.

{|
| [[Image:HOMO-2joshmcicoll.gif|thumb|upright|HOMO-2]]
| [[Image:HOMO-1joshmcncoll.gif|thumb|upright|HOMO-1]]
| [[Image:homojoshmcncoll.gif|thumb|upright|HOMO]]
| [[Image:LUMOjoshmcicoll.gif|thumb|upright|LUMO]]
| [[Image:LUMO+1josmcnicoll.gif|thumb|upright|LUMO+1]]
| [[Image:LUMO+2johmcnicoll.gif|thumb|upright|LUMO+2]]
|}

The calculated approximate molecular orbitals shown above can give an insight in to the control that orbitals are able to have on reactivity. In this case we will be looking at the cycloaddition of dichlorocarbene to the alkene double bond in the starting material.

The approximate molecular orbitals show that in the HOMO of the molecule, there is greater electron density in the alkene double bond endo to the chlorine atom. As this double bond has more electron density in the HOMO than in the bond exo to the chlorine atom, it will be more liable to electrophillic attack than the other double bond.

The intramolecular distances between the exo and endo double bond carbons and the central bridgehead carbon was measured on the geometry optimised model.

{| border="1"
|-
!
! Exo carbon to central bridgehead carbon
! Endo carbon to central bridgehead carbon
|-
! Distance (Angstrom)
| 2.98
| 3.22
|}

The molecule is clearly distorted, with bending of the exo double bond towards the bridgehead carbon to a greater extent than the endo double bond. There is present, an antiperiplanar relationship between the exo pi orbital and the Cl-C sigma* orbital. The interaction would lead to stabilisation of the exo double bond, thus making it less susceptible to eletrophillic attack.

The product from the hydrogenation of the exo double bond was then modelled and was geometrically optimised using the MM2 force field to give an energy of 24.82 kcal/mol.

[[Image:hydroprodjsm08t.gif|alt=Example alt text]]

Both optimised structures were then subjected to a Gaussian calculation in order to calculate the vibrational stretching frequencies and IR spectra:

{|
| [[Image:product12irjsm18.jpg|frame|alt=Example alt text|IR spectrum of 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene]]
| [[Image:hydroprodirjsm18.jpg|frame|alt=Example alt text|IR spectrum of hydrogenated product]]
|}

{| border="1"
|-
!
! 9-ChIoro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene
! Hydrogenated product
|-
! C=C bond stretch frequency (cm-1)
| 1757.4
| 1753.7
|-
! C=C bond stretch frequency (cm-1)
| 1737.1
| -
|-
! C-Cl bond stretch frequency (cm-1)
| 770.9
| 780.4
|}

C-Cl stretching occurs at different frequencies in each of the molecules, with the diene having a lower stretching frequency implying that the bond is weaker. Overlap between C-Cl sigma* and the exo pi orbitals would serve to increase electron density in the C-Cl antibonding orbital thus making it weaker. The exo double bond is not present in the dihydo derivative so no weakening of the C-Cl bond occurs and the bond is stronger, so has a higher stretching frequency.

C=C stretching at 1757 /cm can be attributed to the endo double bond, and is therefore present in both the diene and the dihydro derivative. There is of course an additional C=C stretch in the diene. The frequency of the stretch is lower, indicating a weaker, longer bond. The calculated molecular orbitals would seem to concur with these results. The lower electron density in the exo C=C bond would lead to a weaker bond with lower stretching frequency.

Ajm3081

2011-06-10T12:39:47Z

2011-02-18T12:28:26Z

Ajm308: /* Transition States */

James Marks ( ajm308 / 00548888 ) - {10/02/2011 - 18/02/2011}

=Introduction=

Computations will be carried out in order to characterise the transition states involved in both the Cope rearrangement and the Diels-Alder cycloaddition reactions.

Force field and molecular mechanics methods used in previous experiments are unsuitable for characterising transition states as they are unable to adequately describe the processes of bond making and bond breaking, as well as change in bonding type and electron distribution.

Molecular orbital based methods must be used instead, which involve solving the Schrodinger equation numerically.

Reaction pathways and barrier heights can also be calculated, along with the structures of transitions states.

__TOC__

=Cope Rearrangement=

The Cope rearrangement is an example of a [3,3]-sigmatropic shift rearrangement.

<center> [[Image:ajm308coperearrangement.gif]] </center>

The Cope rearrangement of 1,5-hexadiene will be used as an example, to aid understanding of methods used in investigating chemical reactivity computationally.

The objective is to locate the low energy minima, as well as transition structures on the potential energy surface, in order to determine the preferred reaction mechanism.

It has previously been deduced, both experimentally and computationally, that the reaction proceeds in a concerted fashion via either one of two transition states - the 'chair' or the 'boat':

[[Image:chairconfajm308.png|thumb|center|Chair|]]

[[Image:ajm308boat.png|thumb|center|Boat|]]

==Optimising Reactants and Products==

There a number of possible conformations of 1,5-hexadiene, with each having a distinct total energy.

Initially, 1,5-hexadiene was modeled in GaussView 03 with an 'anti' conformation. This structure was then optimised using the HF/3-21G method and basis set. The optimisation calculation was submitted to Gaussian. Having opened the output files in GaussView 03, the optimised structures were 'symmetrised' in order to determine point group.

The same method was followed on an initially 'gauche' conformation of 1,5-hexadiene. It was anticipated that the 'gauche' conformer would have a higher relative total energy than the 'anti' conformer, on account of the reduced steric repulsion in the arrangement. Initially this assumption was thought to be correct, as the optimised 'gauche' conformer did indeed have a higher relative total energy than the 'anti' conformer. On further investigation, the low energy conformer of 1,5-hexadiene was found to be a 'gauche' example. The lower relative total energy of this conformation can be accounted for by considering the possibility that favourable Van der Waal's interactions between hydrogen atoms are able to override the intrinsic steric strain within the conformation.

As the "anti 2" conformer was not located during initial optimisation, the conformer was modeled in GaussView 03, and optimised to yield the Ci symmetric 'anti' conformer. It was first optimised using the same HF/3-21G protocol, followed by further optimisation with the B3LYP/6-31G protocol. This second protocol is a more computationally intensive optimisation with a larger basis set, and thus could be expected to produce more accurate results.

A summary of the results and characteristics of all aforementioned calculations and conformers is included in the table below:

<center>

{| border="1"
!Conformation
!Theory level
!Computed energy (a.u)
!Appendix Value (a.u)
!Symmetry Point Group
!Structure
!Conformer
|----
|Anti
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 1
|----
|Gauche
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 2
|----
|Lowest Energy Conformer
|HF/3-21G
| -231.69
| -231.69
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 3
|----
|Ci Anti 2 conformation
|HF/3-21G
| -231.69
| -231.69
|Ci
|
|Anti 2
|----
|Ci Anti 2 conformation
|B3LYP/6-31G
| -234.61
| -234.61
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 2
|----
|}

</center>

The two levels of theory, the more advanced B3LYP/6-31G and the more simple HF/3-21G, both returned optimised geometries that are superficially very similar. The difference in relative total energies of the two optimised "Anti 2" conformers was found to be 2.919 a.u.

Closer analysis of the optimised geometries was able to highlight slight differences between the two.

Dihedral angles were compared, as well as bond lengths.

<center>

{| border="1"
!Atoms & Measurement
!HF/3-21G
!B3LYP/6-31G
!Difference
|----
|1,2,3,4 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2,3,4,5 Dihedral angle
|180.0°
|180.0°
|0°
|----
|3,4,5,6 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|1,2 Bond length
|1.316 A
|1.334 A
|0.018 A
|----
|2,3 Bond length
|1.509 A
|1.504 A
|0.005 A
|----
|3,4 Bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

</center>

The more advanced protocol gives dihedral angles and bond lengths which differ from the less advanced protocol, but only to a slight extent, with bond lengths proving more reliable at the HF/3-21G level than the dihedral angles.

===Frequency Calculations===

The B3LYP/6-31G optimised was then submitted to frequency calculations.

Frequency calculations, as shown in previous modules, are able to confirm that a minimum has been reached, by showing that all vibrational frequencies are positive and real.

Following frequency calculations at the same level of theory, the vibrational frequencies were all confirmed to be positive and real, with the computed IR Spectra shown below:

<center> [[Image:AJMIRSpectra.jpg]] </center>

The output file was then used to find Thermochemical data. Four pieces of important data were noted.

A = The potential energy at 0 K, including zero-point vibrational energy. (E = Eelec + ZPE)

B = The energy at 298.15 K, 1 atm, including contributions from Translation, Rotational and Vibrational energy modes. (E = E + Evib + Erot + Etrans)

C = A correction for RT. (H = E + RT)

D = Includes the entropic contribution to free energy. (G = H - TS)

A. Sum of Electronic and Zero Point Energies: -234.47 a.u

B. Sum of Electronic and Thermal Energies: -234.46 a.u

C. Sum of Electronic and Thermal Enthalpies: -234.46 a.u

D. Sum of Electronic and Thermal Free Energies: -234.50 a.u

==Chair and Boat Transition Structures==

===Chair===

Initially an allyl (CH2CHCH2) fragment was modeled in GaussView 03, and optimised using the HF/3-21G protocol. The optimised fragment was then reproduced twice and the fragments were orientated such that they imitated the chair transition state.

This transition state was then manually optimised using two alternative methods. The optimisations become difficult as in order to compute, it is necessary for the method to have "knowledge" of where the negative direction of curvature (the reaction coordinate) is. Providing a reasonable guess has been made, the easiest way to obtain the required information is to compute the force constant matrix in the initial step of an optimisation, which can be updated as the optimisation proceeds. In some cases it is possible to generate a more accurate transition structure by freezing the reaction coordinate. Once the molecule is fully relaxed, reaction coordinate constraints can be removed, followed by optimisation of the transition state.

====Optimisation to a TS (Berny)====

The approximated transition state structure was optimised using the HF/3-21G protocol. The Job Type was chosen as 'Opt+Freq' and the method was further modified by changing 'Optimization to a Minimum' to 'Optimization to a TS (Berny)'. Force constants were set to calculate only once.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:imaginaryfrequencycopeajm308.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Frozen Coordinate Method====

The optimisation was then carried out using the frozen coordinate method. The approximated transition state structure was again used. The method outlined @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was followed.

On completion of the submitted job, the output showed that the optimised structure was very similar to that found using the 'Optimisation to TS (Berny)' method, however it is noted that bond breaking/forming distances are fixed at 2.2 A. The constraints imposed before submitting the job were removed, and the transition state was optimised again.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:AJM308FrozenMethod.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Comparison====

The two methods concur.

Although the two methods were both successful in this case, there are advantages and disadvantages to both.

The 'Optimisation to TS (Berny)' method requires an accurate approximate transition state in order to yield accurate results. For the simple case above this was relatively easy, however, in more complex systems it may not be as simple.

Although the frozen coordinate method does not require as accurate an initial transition state as the 'Optimisation to TS (Berny)' method, it is more computationally expensive.

===Boat===

Another method was then used to optimise the boat transition state. The method utilised was the QST2 method. Reactants and products are specified for the reaction and a computational interpolation will attempt to locate the transition state.

Again, the method located @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was adhered to in order to prepare a Gaussian Input File.

The first QST2 calculation was then initiated. The Job Type was altered to 'Opt+Freq' and 'Optimise to a TS (QST2)'. This job was then submitted and failed. This failure highlights an inherent deficiency in the capability of computational chemistry. If the input file does not contain all the information required by the computational method, it will not succeed.

In order for the method to succeed the reactant and product geometries needed to be altered so that they more closely resemble the boat transition structure. The geometries were altered, with the central C-C-C-C dihedral angle being set to 0 o and the inside C-C-C angles set to 100 o.

The job was then resubmitted.

Only one imaginary vibrational frequency was returned, -840 cm-1 and the motion is shown below:

<center> [[Image:AJM308Boat.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.14 A.

The Energy of the transition state was found to be -231.60 a.u.

===Intrinsic Reaction Coordinate Method===

This method allows the following of the minimum energy path from the transition structure to its local minimum on the potential energy surface. A series of points is produced by taking small geometry steps in the direction of the steepest energy gradient. Initially it was chosen to run the method across 50 points on the potential energy surface, for both the chair and the boat transition states. The computation was run only in the forward direction due to the symmetry of the potential energy surface in this example. However, standard protocol is to run the method in both the forward and backward directions.

====Chair====

On opening the output file it was observed that no minimum had been reached in the computation.

Three options are then available:

1. Take the last point on the initial IRC and run a normal minimisation.

2. Restart the IRC and run with a larger number of points.

3. Specify that force constants should be computed at each step.

Approach 1 would be the least computationally costly, but the wrong minima may be found. Approach 2 is more reliable, but again, problems related to finding the wrong structure can present if too many points are required. Approach 3 is the most computationally expensive, but also the most reliable. It was decided to complete the IRC method using approached 1 and 3. The results for the chair transition state are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.62
|[[Image:ajm308chairirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.70
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.69
|[[Image:ajm308chairirc2.jpg|thumb|left|]]
|Minimum found.
|----
|}

</center>

Approach 1 yielded the lowest energy minima, with the method being far more efficient than Approach 3. The chair transition structure was shown to minimise to the 'Gauche 2' conformation.

====Boat====

The same methodology was applied to the Boat transition structure. Results are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.68
|[[Image:ajm308boatirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.68
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.65
|[[Image:ajm308boatirc2.jpg|thumb|left|]]
|Minimum not found.
|----
|}

</center>

===Further Analysis===

Both the Chair and Boat transition structures were reoptimised using the more advanced B3LYP/6-31G protocol, with frequency analysis also being performed. The two methods utilised are compared in the tables below:

<center>

{| border="1"
!colspan="3"|'''Chair'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G
|----
|Energy (a.u)
| -231.61
| -234.56
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (a.u)
| -231.60
| -234.54
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

</center>

Results show that the change to a more comprehensive method has little effect on the geometries of the transition states, as defined by bond angles, bond lengths and inter-fragment distances.

However, there is quite a marked difference between the total relative energy of the transition structures.

====Thermochemical Data====

'''Chair TS - HF/3-21G'''

A. -231.47 a.u

B. -231.46 a.u

C. -231.46 a.u

D. -231.50 a.u

'''Chair TS - B3LYP/6-31G'''

A. -234.41 a.u

B. -234.41 a.u

C. -234.41 a.u

D. -234.44 a.u

'''Boat TS - HF/3-21G'''

A. -231.45 a.u

B. -231.45 a.u

C. -231.44 a.u

D. -231.48 a.u

'''Boat TS - B3LYP/6-31G'''

A. -234.40 a.u

B. -234.40 a.u

C. -234.40 a.u

D. -234.43 a.u

{Where A,B,C and D are defined as earlier}

These values correlate well with those found @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]

Using these values it was possible to calculate activation energies, as shown in the table below:

<center>

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

</center>

Values calculated with the more advanced methodology are closer to experimental values than those calculated with the HF/3-21G level of theory.

The chair transition state has a lower activation energy than the boat transition state, in agreement with the literature <ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. This is on account of the reduced steric hindrance encountered proceeding via the chair transition state than the boat transition state.

=Diels Alder Cyclo-Addition=

The Diels-Alder cycloaddition occurs between a diene and a dienophile, with a wide range of molecules able to take on each role, and is an example of a pericyclic reaction. The reaction is only allowed (ie. not forbidden) if the HOMO of one reactant is able to interact with the LUMO of the other. There must be sufficient orbital overlap for the reaction to be allowed, and as such the symmetry properties of the orbitals in question must be identical.

A substituted dienophile can invoke secondary orbital effects, resulting in regioselectivity.

The simplest Diels-Alder reaction is that which occurs between ethene (the dienophile) and cis-butadiene (the diene).

<center> [[Image:Mb da3.jpg|thumb|center|]] </center>

Principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] as the diene, butadiene, has 4 π orbitals in its π system.

==Ethene and cis-Butadiene==

cis-Butadiene and ethene were modeled in GaussView 03, and optimised in Gaussian. The semi-empirical AM1 method was utilised and the molecular orbitals were visualised and are illustrated below:

Relative energy, and symmetry in relation to the σv plane are also indicated.

<center>

{| border="1"
!Molecule
!Total Energy of Molecule (a.u)
!HOMO energy (a.u)
!Visualised HOMO
!HOMO Symmetry (with respect to σv plane)
!LUMO Energy (a.u)
!Visualised LUMO
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.026
| -0.39
|[[Image:ajm308EtheneHOMO.jpg|thumb|]]
|Symmetric
|0.052
|[[Image:ajm308EtheneLUMO.jpg|thumb|]]
|Antisymmetric
|----
|Cis-butadiene
|0.049
| -0.34
|[[Image:ajm308CBHOMO.jpg|thumb|]]
|Antisymmetric
|0.017
|[[Image:ajm308CBLUMO.jpg|thumb|]]
|Symmetric
|----
|}

</center>

Only orbitals of identical symmetry have the required overlap density for the reaction to proceed, and so it can be seen that the HOMO of cis-butadiene can interact with the LUMO of ethene, and vice versa.

===Transition States===

The overlap between the two sets of pi orbitals is maximised by adopting an envelope type structure. In order to obtain the starting geometry a bicyclic system was modeled, and the -CH2-CH2- fragment removed. Inter-fragment distance was then guessed to be 2.15 A.

Optimisation was then carried out, using methodology similar to that found in Section xxx above.

One imaginary frequency was found to be -818 cm-1. This vibration is visualised below and shows synchronous bond forming, concurring with the concerted nature of pericyclic reactions.

<center>

[[Image:DAvibsajm308.gif]]

</center>

The lowest real vibrational frequency is observed at 167 cm-1 and is attributed to the rocking of the CH2=CH2 section of the transition structure.

The energy of the transition structure was found to be -231.60 a.u.

The HOMO and LUMO of the transition state were also visualised and are shown below:

<center>

[[Image:HOMODAajm308.jpg|thumb|center|]]

[[Image:LUMODAajm308.jpg|thumb|center|]]

</center>

The HOMO is antisymmetric, and can be associated with overlap of the HOMO of cis-butadiene and the LUMO of ethene - where two antisymmetric molecular orbitals overlap.

Similarly, the LUMO is symmetric, and can be associated with overlap of the LUMO of cis-butadiene and the HOMO of ethene.

The geometry of the transition structure is outlined in the table below.

<center>

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C Length
| -
|2.21 A
|----
|Ethene C=C Length
|1.33 A
|1.38 A
|----
|Butadiene C=C Length
|1.34 A
|1.37 A
|----
|Butadiene C-C Length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C Angle
|125.6°
|121.5°
|----
|}

</center>

The C-C, that is only partially formed in the transition state, is markedly longer than any other bond present as a result of this. C-C and C=C bonds are no longer differentiable in the transition state, as they are in the reactants. Typical sp3 C-C bond lengths of 1.54 A <ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref> correlate well with the calculated C-C bond distance in butadiene. Calculated sp2 C=C bond lengths of 1.34 A and 1.33 A correlate very well with the typical values.

The Van der Waal's radius of the C atom is 1.7 A. <ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

==Cyclohexa-1,3-diene with Maleic Anhydride==

The reaction of cyclohexa-1,3-diene and maleic anhydride yields the endo product in majority. The reaction proceeds under kinetic control so it assumed that the exo transition state is at higher energy.

[[Image:Ajm308reactionscheme.gif|center|]]

===Transition States===

Again, bicyclic systems were used in order to model the transition states for both the endo and exo products. 2.2 A was used as an initial guess for the inter-fragment distances, and both structures were optimised using the 'Optimisation to TS (Berny)' method, as outlined in section xxx above.

Frequency analysis was also performed.

Geometric and thermochemical properties, as well as the imaginary vibrational motions returned are displayed in the table below:

<center>

{| border="1"
|Property
|Exo
|Endo
|----
|Product Energy (a.u)
| -0.16
| -0.16
|----
|Transition State Energy (a.u)
| -0.051
| -0.052
|----
|Imaginary Vibrational Frequency (cm-1)
| -812
| -806
|----
|Imaginary Vibration Animation
|[[Image:EXOVIbajm308.gif|thumb|left|350px|]]
|[[Image:ENDOVIBajm308.gif|thumb|left|350px|]]
|----
|Lowest Real Frequency (cm-1)
|61
|62
|----
|Lowest Real Frequency Assignment
|Rocking of Cyclohexadiene Fragment
|Rocking of Cyclohexadiene Fragment
|----
|Fragment Bond Distance (A)
|2.17
|2.16
|----
|(C=O)-C-(C=O) Through Space Distance (A)
|2.28
|2.28
|----
|C=C Distance (A)
|1.40
|1.40
|----
|C-C Bridge Distance (A)
|1.52
|1.52
|----
|HOMO
|[[Image:EXOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|LUMO
|[[Image:EXOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|}

</center>

The thermochemical properties are in agreement with the prediction that the endo product will be major, the exo minor. The endo transition state has a lower transition state than the exo transition state, and as the reaction is under kinetic control, is favoured as the reaction energy barrier is smaller.

The HOMOs visualised above show differences between the endo and exo transition states, in the -(C=O)-O-(C=O)- region. The endo transition state has appreciable electron density in the region, however, the exo transition state does not. There is clearly more secondary orbital effects operating in the endo transition state, than in the exo transition state. The transition state is stabilised by these interactions, thus lowering the energy of the endo transition state relative to the exo transition state.

=Conclusions=

Once again, the power of computational chemistry is apparent, as is the need to balance the desired accuracy of the calculations against computational cost and time constraints. One example is when using the QST2 method which is more efficient than the QST3 method, but has the potential to fail if reactants and products are not close to the transition structure. It seems it is often worth utilising a lower level protocol initially, and if the desired results are not obtained, then a higher level calculation should be carried out.

The wide range of information gleaned from the computational methods, and close correlation with experimental results, means computational chemistry rightly deserves a place alongside more traditional methods of experimentation.

Limitations of the field are also apparent in accounting for more complex physical phenomena, such as solvent effects.

=References=

<references/>

Rep:Mod:ajm3081989

2011-02-18T12:28:05Z

Ajm308: /* Transition States */

James Marks ( ajm308 / 00548888 ) - {10/02/2011 - 18/02/2011}

=Introduction=

Computations will be carried out in order to characterise the transition states involved in both the Cope rearrangement and the Diels-Alder cycloaddition reactions.

Force field and molecular mechanics methods used in previous experiments are unsuitable for characterising transition states as they are unable to adequately describe the processes of bond making and bond breaking, as well as change in bonding type and electron distribution.

Molecular orbital based methods must be used instead, which involve solving the Schrodinger equation numerically.

Reaction pathways and barrier heights can also be calculated, along with the structures of transitions states.

__TOC__

=Cope Rearrangement=

The Cope rearrangement is an example of a [3,3]-sigmatropic shift rearrangement.

<center> [[Image:ajm308coperearrangement.gif]] </center>

The Cope rearrangement of 1,5-hexadiene will be used as an example, to aid understanding of methods used in investigating chemical reactivity computationally.

The objective is to locate the low energy minima, as well as transition structures on the potential energy surface, in order to determine the preferred reaction mechanism.

It has previously been deduced, both experimentally and computationally, that the reaction proceeds in a concerted fashion via either one of two transition states - the 'chair' or the 'boat':

[[Image:chairconfajm308.png|thumb|center|Chair|]]

[[Image:ajm308boat.png|thumb|center|Boat|]]

==Optimising Reactants and Products==

There a number of possible conformations of 1,5-hexadiene, with each having a distinct total energy.

Initially, 1,5-hexadiene was modeled in GaussView 03 with an 'anti' conformation. This structure was then optimised using the HF/3-21G method and basis set. The optimisation calculation was submitted to Gaussian. Having opened the output files in GaussView 03, the optimised structures were 'symmetrised' in order to determine point group.

The same method was followed on an initially 'gauche' conformation of 1,5-hexadiene. It was anticipated that the 'gauche' conformer would have a higher relative total energy than the 'anti' conformer, on account of the reduced steric repulsion in the arrangement. Initially this assumption was thought to be correct, as the optimised 'gauche' conformer did indeed have a higher relative total energy than the 'anti' conformer. On further investigation, the low energy conformer of 1,5-hexadiene was found to be a 'gauche' example. The lower relative total energy of this conformation can be accounted for by considering the possibility that favourable Van der Waal's interactions between hydrogen atoms are able to override the intrinsic steric strain within the conformation.

As the "anti 2" conformer was not located during initial optimisation, the conformer was modeled in GaussView 03, and optimised to yield the Ci symmetric 'anti' conformer. It was first optimised using the same HF/3-21G protocol, followed by further optimisation with the B3LYP/6-31G protocol. This second protocol is a more computationally intensive optimisation with a larger basis set, and thus could be expected to produce more accurate results.

A summary of the results and characteristics of all aforementioned calculations and conformers is included in the table below:

<center>

{| border="1"
!Conformation
!Theory level
!Computed energy (a.u)
!Appendix Value (a.u)
!Symmetry Point Group
!Structure
!Conformer
|----
|Anti
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 1
|----
|Gauche
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 2
|----
|Lowest Energy Conformer
|HF/3-21G
| -231.69
| -231.69
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 3
|----
|Ci Anti 2 conformation
|HF/3-21G
| -231.69
| -231.69
|Ci
|
|Anti 2
|----
|Ci Anti 2 conformation
|B3LYP/6-31G
| -234.61
| -234.61
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 2
|----
|}

</center>

The two levels of theory, the more advanced B3LYP/6-31G and the more simple HF/3-21G, both returned optimised geometries that are superficially very similar. The difference in relative total energies of the two optimised "Anti 2" conformers was found to be 2.919 a.u.

Closer analysis of the optimised geometries was able to highlight slight differences between the two.

Dihedral angles were compared, as well as bond lengths.

<center>

{| border="1"
!Atoms & Measurement
!HF/3-21G
!B3LYP/6-31G
!Difference
|----
|1,2,3,4 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2,3,4,5 Dihedral angle
|180.0°
|180.0°
|0°
|----
|3,4,5,6 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|1,2 Bond length
|1.316 A
|1.334 A
|0.018 A
|----
|2,3 Bond length
|1.509 A
|1.504 A
|0.005 A
|----
|3,4 Bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

</center>

The more advanced protocol gives dihedral angles and bond lengths which differ from the less advanced protocol, but only to a slight extent, with bond lengths proving more reliable at the HF/3-21G level than the dihedral angles.

===Frequency Calculations===

The B3LYP/6-31G optimised was then submitted to frequency calculations.

Frequency calculations, as shown in previous modules, are able to confirm that a minimum has been reached, by showing that all vibrational frequencies are positive and real.

Following frequency calculations at the same level of theory, the vibrational frequencies were all confirmed to be positive and real, with the computed IR Spectra shown below:

<center> [[Image:AJMIRSpectra.jpg]] </center>

The output file was then used to find Thermochemical data. Four pieces of important data were noted.

A = The potential energy at 0 K, including zero-point vibrational energy. (E = Eelec + ZPE)

B = The energy at 298.15 K, 1 atm, including contributions from Translation, Rotational and Vibrational energy modes. (E = E + Evib + Erot + Etrans)

C = A correction for RT. (H = E + RT)

D = Includes the entropic contribution to free energy. (G = H - TS)

A. Sum of Electronic and Zero Point Energies: -234.47 a.u

B. Sum of Electronic and Thermal Energies: -234.46 a.u

C. Sum of Electronic and Thermal Enthalpies: -234.46 a.u

D. Sum of Electronic and Thermal Free Energies: -234.50 a.u

==Chair and Boat Transition Structures==

===Chair===

Initially an allyl (CH2CHCH2) fragment was modeled in GaussView 03, and optimised using the HF/3-21G protocol. The optimised fragment was then reproduced twice and the fragments were orientated such that they imitated the chair transition state.

This transition state was then manually optimised using two alternative methods. The optimisations become difficult as in order to compute, it is necessary for the method to have "knowledge" of where the negative direction of curvature (the reaction coordinate) is. Providing a reasonable guess has been made, the easiest way to obtain the required information is to compute the force constant matrix in the initial step of an optimisation, which can be updated as the optimisation proceeds. In some cases it is possible to generate a more accurate transition structure by freezing the reaction coordinate. Once the molecule is fully relaxed, reaction coordinate constraints can be removed, followed by optimisation of the transition state.

====Optimisation to a TS (Berny)====

The approximated transition state structure was optimised using the HF/3-21G protocol. The Job Type was chosen as 'Opt+Freq' and the method was further modified by changing 'Optimization to a Minimum' to 'Optimization to a TS (Berny)'. Force constants were set to calculate only once.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:imaginaryfrequencycopeajm308.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Frozen Coordinate Method====

The optimisation was then carried out using the frozen coordinate method. The approximated transition state structure was again used. The method outlined @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was followed.

On completion of the submitted job, the output showed that the optimised structure was very similar to that found using the 'Optimisation to TS (Berny)' method, however it is noted that bond breaking/forming distances are fixed at 2.2 A. The constraints imposed before submitting the job were removed, and the transition state was optimised again.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:AJM308FrozenMethod.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Comparison====

The two methods concur.

Although the two methods were both successful in this case, there are advantages and disadvantages to both.

The 'Optimisation to TS (Berny)' method requires an accurate approximate transition state in order to yield accurate results. For the simple case above this was relatively easy, however, in more complex systems it may not be as simple.

Although the frozen coordinate method does not require as accurate an initial transition state as the 'Optimisation to TS (Berny)' method, it is more computationally expensive.

===Boat===

Another method was then used to optimise the boat transition state. The method utilised was the QST2 method. Reactants and products are specified for the reaction and a computational interpolation will attempt to locate the transition state.

Again, the method located @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was adhered to in order to prepare a Gaussian Input File.

The first QST2 calculation was then initiated. The Job Type was altered to 'Opt+Freq' and 'Optimise to a TS (QST2)'. This job was then submitted and failed. This failure highlights an inherent deficiency in the capability of computational chemistry. If the input file does not contain all the information required by the computational method, it will not succeed.

In order for the method to succeed the reactant and product geometries needed to be altered so that they more closely resemble the boat transition structure. The geometries were altered, with the central C-C-C-C dihedral angle being set to 0 o and the inside C-C-C angles set to 100 o.

The job was then resubmitted.

Only one imaginary vibrational frequency was returned, -840 cm-1 and the motion is shown below:

<center> [[Image:AJM308Boat.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.14 A.

The Energy of the transition state was found to be -231.60 a.u.

===Intrinsic Reaction Coordinate Method===

This method allows the following of the minimum energy path from the transition structure to its local minimum on the potential energy surface. A series of points is produced by taking small geometry steps in the direction of the steepest energy gradient. Initially it was chosen to run the method across 50 points on the potential energy surface, for both the chair and the boat transition states. The computation was run only in the forward direction due to the symmetry of the potential energy surface in this example. However, standard protocol is to run the method in both the forward and backward directions.

====Chair====

On opening the output file it was observed that no minimum had been reached in the computation.

Three options are then available:

1. Take the last point on the initial IRC and run a normal minimisation.

2. Restart the IRC and run with a larger number of points.

3. Specify that force constants should be computed at each step.

Approach 1 would be the least computationally costly, but the wrong minima may be found. Approach 2 is more reliable, but again, problems related to finding the wrong structure can present if too many points are required. Approach 3 is the most computationally expensive, but also the most reliable. It was decided to complete the IRC method using approached 1 and 3. The results for the chair transition state are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.62
|[[Image:ajm308chairirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.70
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.69
|[[Image:ajm308chairirc2.jpg|thumb|left|]]
|Minimum found.
|----
|}

</center>

Approach 1 yielded the lowest energy minima, with the method being far more efficient than Approach 3. The chair transition structure was shown to minimise to the 'Gauche 2' conformation.

====Boat====

The same methodology was applied to the Boat transition structure. Results are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.68
|[[Image:ajm308boatirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.68
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.65
|[[Image:ajm308boatirc2.jpg|thumb|left|]]
|Minimum not found.
|----
|}

</center>

===Further Analysis===

Both the Chair and Boat transition structures were reoptimised using the more advanced B3LYP/6-31G protocol, with frequency analysis also being performed. The two methods utilised are compared in the tables below:

<center>

{| border="1"
!colspan="3"|'''Chair'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G
|----
|Energy (a.u)
| -231.61
| -234.56
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (a.u)
| -231.60
| -234.54
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

</center>

Results show that the change to a more comprehensive method has little effect on the geometries of the transition states, as defined by bond angles, bond lengths and inter-fragment distances.

However, there is quite a marked difference between the total relative energy of the transition structures.

====Thermochemical Data====

'''Chair TS - HF/3-21G'''

A. -231.47 a.u

B. -231.46 a.u

C. -231.46 a.u

D. -231.50 a.u

'''Chair TS - B3LYP/6-31G'''

A. -234.41 a.u

B. -234.41 a.u

C. -234.41 a.u

D. -234.44 a.u

'''Boat TS - HF/3-21G'''

A. -231.45 a.u

B. -231.45 a.u

C. -231.44 a.u

D. -231.48 a.u

'''Boat TS - B3LYP/6-31G'''

A. -234.40 a.u

B. -234.40 a.u

C. -234.40 a.u

D. -234.43 a.u

{Where A,B,C and D are defined as earlier}

These values correlate well with those found @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]

Using these values it was possible to calculate activation energies, as shown in the table below:

<center>

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

</center>

Values calculated with the more advanced methodology are closer to experimental values than those calculated with the HF/3-21G level of theory.

The chair transition state has a lower activation energy than the boat transition state, in agreement with the literature <ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. This is on account of the reduced steric hindrance encountered proceeding via the chair transition state than the boat transition state.

=Diels Alder Cyclo-Addition=

The Diels-Alder cycloaddition occurs between a diene and a dienophile, with a wide range of molecules able to take on each role, and is an example of a pericyclic reaction. The reaction is only allowed (ie. not forbidden) if the HOMO of one reactant is able to interact with the LUMO of the other. There must be sufficient orbital overlap for the reaction to be allowed, and as such the symmetry properties of the orbitals in question must be identical.

A substituted dienophile can invoke secondary orbital effects, resulting in regioselectivity.

The simplest Diels-Alder reaction is that which occurs between ethene (the dienophile) and cis-butadiene (the diene).

<center> [[Image:Mb da3.jpg|thumb|center|]] </center>

Principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] as the diene, butadiene, has 4 π orbitals in its π system.

==Ethene and cis-Butadiene==

cis-Butadiene and ethene were modeled in GaussView 03, and optimised in Gaussian. The semi-empirical AM1 method was utilised and the molecular orbitals were visualised and are illustrated below:

Relative energy, and symmetry in relation to the σv plane are also indicated.

<center>

{| border="1"
!Molecule
!Total Energy of Molecule (a.u)
!HOMO energy (a.u)
!Visualised HOMO
!HOMO Symmetry (with respect to σv plane)
!LUMO Energy (a.u)
!Visualised LUMO
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.026
| -0.39
|[[Image:ajm308EtheneHOMO.jpg|thumb|]]
|Symmetric
|0.052
|[[Image:ajm308EtheneLUMO.jpg|thumb|]]
|Antisymmetric
|----
|Cis-butadiene
|0.049
| -0.34
|[[Image:ajm308CBHOMO.jpg|thumb|]]
|Antisymmetric
|0.017
|[[Image:ajm308CBLUMO.jpg|thumb|]]
|Symmetric
|----
|}

</center>

Only orbitals of identical symmetry have the required overlap density for the reaction to proceed, and so it can be seen that the HOMO of cis-butadiene can interact with the LUMO of ethene, and vice versa.

===Transition States===

The overlap between the two sets of pi orbitals is maximised by adopting an envelope type structure. In order to obtain the starting geometry a bicyclic system was modeled, and the -CH2-CH2- fragment removed. Inter-fragment distance was then guessed to be 2.15 A.

Optimisation was then carried out, using methodology similar to that found in Section xxx above.

One imaginary frequency was found to be -818 cm-1. This vibration is visualised below and shows synchronous bond forming, concurring with the concerted nature of pericyclic reactions.

<center>

[[Image:DAvibsajm308.gif]]

</center>

The lowest real vibrational frequency is observed at 167 cm-1 and is attributed to the rocking of the CH2=CH2 section of the transition structure.

The energy of the transition structure was found to be -231.60 a.u.

The HOMO and LUMO of the transition state were also visualised and are shown below:

<center>

[[Image:HOMODAajm308.jpg|thumb|center|]]

[[Image:LUMODAajm308.jpg|thumb|center|]]

</center>

The HOMO is antisymmetric, and can be associated with overlap of the HOMO of cis-butadiene and the LUMO of ethene - where two antisymmetric molecular orbitals overlap.

Similarly, the LUMO is symmetric, and can be associated with overlap of the LUMO of cis-butadiene and the HOMO of ethene.

The geometry of the transition structure is outlined in the table below.

<center>

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C Length
| -
|2.21 A
|----
|Ethene C=C Length
|1.33 A
|1.38 A
|----
|Butadiene C=C Length
|1.34 A
|1.37 A
|----
|Butadiene C-C Length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C Angle
|125.6°
|121.5°
|----
|}

</center>

The C-C, that is only partially formed in the transition state, is markedly longer than any other bond present as a result of this. C-C and C=C bonds are no longer differentiable in the transition state, as they are in the reactants. Typical sp3 C-C bond lengths of 1.54 A <ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref> correlate well with the calculated C-C bond distance in butadiene. Calculated sp2 C=C bond lengths of 1.34 A and 1.33 A correlate very well with the typical values.

The Van der Waal's radius of the C atom is 1.7 A. <ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

==Cyclohexa-1,3-diene with Maleic Anhydride==

The reaction of cyclohexa-1,3-diene and maleic anhydride yields the endo product in majority. The reaction proceeds under kinetic control so it assumed that the exo transition state is at higher energy.

[[Image:Ajm308reactionscheme.gif|center|]]

===Transition States===

Again, bicyclic systems were used in order to model the transition states for both the endo and exo products. 2.2 A was used as an initial guess for the inter-fragment distances, and both structures were optimised using the 'Optimisation to TS (Berny)' method, as outlined in section xxx above.

Frequency analysis was also performed.

Geometric and thermochemical properties, as well as the imaginary vibrational motions returned are displayed in the table below:

<center>

{| border="1"
|Property
|Exo
|Endo
|----
|Product Energy (a.u)
| -0.16
| -0.16
|----
|Transition State Energy (a.u)
| -0.051
| -0.052
|----
|Imaginary Vibrational Frequency (cm-1)
| -812
| -806
|----
|Imaginary Vibration Animation
|[[Image:EXOVIbajm308.gif|thumb|left|350px|]]
|[[Image:ENDOVIBajm308.gif|thumb|left|350px|]]
|----
|Lowest Real Frequency (cm-1)
|61
|62
|----
|Lowest Real Frequency Assignment
|Rocking of Cyclohexadiene Fragment
|Rocking of Cyclohexadiene Fragment
|----
|Fragment Bond Distance (A)
|2.17
|2.16
|----
|(C=O)-C-(C=O) Through Space Distance (A)
|2.28
|2.28
|----
|C=C Distance (A)
|1.40
|1.40
|----
|C-C Bridge Distance (A)
|1.52
|1.52
|----
|HOMO
|[[Image:EXOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|LUMO
|[[Image:EXOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|}

</center>

The thermochemical properties are in agreement with the prediction that the endo product will be major, the exo minor. The endo transition state has a lower transition state than the exo transition state, and as the reaction is under kinetic control, is favoured as the reaction energy barrier is smaller.

The HOMOs visualised above show differences between the endo and exo transition states, in the -(C=O)-O-(C=O)- region. The endo transition state has appreciable electron density in the region, however, the exo transition state does not. There is clearly more secondary orbital effects operating in the endo transition state, than in the exo transition state. The transition state is stabilised by these interactions, thus lowering the energy of the endo transition state relative to the exo transition state. This secondary orbital interaction is shown in the diagram below:

!!!Diagram!!!

=Conclusions=

Once again, the power of computational chemistry is apparent, as is the need to balance the desired accuracy of the calculations against computational cost and time constraints. One example is when using the QST2 method which is more efficient than the QST3 method, but has the potential to fail if reactants and products are not close to the transition structure. It seems it is often worth utilising a lower level protocol initially, and if the desired results are not obtained, then a higher level calculation should be carried out.

The wide range of information gleaned from the computational methods, and close correlation with experimental results, means computational chemistry rightly deserves a place alongside more traditional methods of experimentation.

Limitations of the field are also apparent in accounting for more complex physical phenomena, such as solvent effects.

=References=

<references/>

Rep:Mod:ajm3081989

2011-02-18T12:25:28Z

Ajm308: /* Transition States */

James Marks ( ajm308 / 00548888 ) - {10/02/2011 - 18/02/2011}

=Introduction=

Computations will be carried out in order to characterise the transition states involved in both the Cope rearrangement and the Diels-Alder cycloaddition reactions.

Force field and molecular mechanics methods used in previous experiments are unsuitable for characterising transition states as they are unable to adequately describe the processes of bond making and bond breaking, as well as change in bonding type and electron distribution.

Molecular orbital based methods must be used instead, which involve solving the Schrodinger equation numerically.

Reaction pathways and barrier heights can also be calculated, along with the structures of transitions states.

__TOC__

=Cope Rearrangement=

The Cope rearrangement is an example of a [3,3]-sigmatropic shift rearrangement.

<center> [[Image:ajm308coperearrangement.gif]] </center>

The Cope rearrangement of 1,5-hexadiene will be used as an example, to aid understanding of methods used in investigating chemical reactivity computationally.

The objective is to locate the low energy minima, as well as transition structures on the potential energy surface, in order to determine the preferred reaction mechanism.

It has previously been deduced, both experimentally and computationally, that the reaction proceeds in a concerted fashion via either one of two transition states - the 'chair' or the 'boat':

[[Image:chairconfajm308.png|thumb|center|Chair|]]

[[Image:ajm308boat.png|thumb|center|Boat|]]

==Optimising Reactants and Products==

There a number of possible conformations of 1,5-hexadiene, with each having a distinct total energy.

Initially, 1,5-hexadiene was modeled in GaussView 03 with an 'anti' conformation. This structure was then optimised using the HF/3-21G method and basis set. The optimisation calculation was submitted to Gaussian. Having opened the output files in GaussView 03, the optimised structures were 'symmetrised' in order to determine point group.

The same method was followed on an initially 'gauche' conformation of 1,5-hexadiene. It was anticipated that the 'gauche' conformer would have a higher relative total energy than the 'anti' conformer, on account of the reduced steric repulsion in the arrangement. Initially this assumption was thought to be correct, as the optimised 'gauche' conformer did indeed have a higher relative total energy than the 'anti' conformer. On further investigation, the low energy conformer of 1,5-hexadiene was found to be a 'gauche' example. The lower relative total energy of this conformation can be accounted for by considering the possibility that favourable Van der Waal's interactions between hydrogen atoms are able to override the intrinsic steric strain within the conformation.

As the "anti 2" conformer was not located during initial optimisation, the conformer was modeled in GaussView 03, and optimised to yield the Ci symmetric 'anti' conformer. It was first optimised using the same HF/3-21G protocol, followed by further optimisation with the B3LYP/6-31G protocol. This second protocol is a more computationally intensive optimisation with a larger basis set, and thus could be expected to produce more accurate results.

A summary of the results and characteristics of all aforementioned calculations and conformers is included in the table below:

<center>

{| border="1"
!Conformation
!Theory level
!Computed energy (a.u)
!Appendix Value (a.u)
!Symmetry Point Group
!Structure
!Conformer
|----
|Anti
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 1
|----
|Gauche
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 2
|----
|Lowest Energy Conformer
|HF/3-21G
| -231.69
| -231.69
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 3
|----
|Ci Anti 2 conformation
|HF/3-21G
| -231.69
| -231.69
|Ci
|
|Anti 2
|----
|Ci Anti 2 conformation
|B3LYP/6-31G
| -234.61
| -234.61
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 2
|----
|}

</center>

The two levels of theory, the more advanced B3LYP/6-31G and the more simple HF/3-21G, both returned optimised geometries that are superficially very similar. The difference in relative total energies of the two optimised "Anti 2" conformers was found to be 2.919 a.u.

Closer analysis of the optimised geometries was able to highlight slight differences between the two.

Dihedral angles were compared, as well as bond lengths.

<center>

{| border="1"
!Atoms & Measurement
!HF/3-21G
!B3LYP/6-31G
!Difference
|----
|1,2,3,4 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2,3,4,5 Dihedral angle
|180.0°
|180.0°
|0°
|----
|3,4,5,6 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|1,2 Bond length
|1.316 A
|1.334 A
|0.018 A
|----
|2,3 Bond length
|1.509 A
|1.504 A
|0.005 A
|----
|3,4 Bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

</center>

The more advanced protocol gives dihedral angles and bond lengths which differ from the less advanced protocol, but only to a slight extent, with bond lengths proving more reliable at the HF/3-21G level than the dihedral angles.

===Frequency Calculations===

The B3LYP/6-31G optimised was then submitted to frequency calculations.

Frequency calculations, as shown in previous modules, are able to confirm that a minimum has been reached, by showing that all vibrational frequencies are positive and real.

Following frequency calculations at the same level of theory, the vibrational frequencies were all confirmed to be positive and real, with the computed IR Spectra shown below:

<center> [[Image:AJMIRSpectra.jpg]] </center>

The output file was then used to find Thermochemical data. Four pieces of important data were noted.

A = The potential energy at 0 K, including zero-point vibrational energy. (E = Eelec + ZPE)

B = The energy at 298.15 K, 1 atm, including contributions from Translation, Rotational and Vibrational energy modes. (E = E + Evib + Erot + Etrans)

C = A correction for RT. (H = E + RT)

D = Includes the entropic contribution to free energy. (G = H - TS)

A. Sum of Electronic and Zero Point Energies: -234.47 a.u

B. Sum of Electronic and Thermal Energies: -234.46 a.u

C. Sum of Electronic and Thermal Enthalpies: -234.46 a.u

D. Sum of Electronic and Thermal Free Energies: -234.50 a.u

==Chair and Boat Transition Structures==

===Chair===

Initially an allyl (CH2CHCH2) fragment was modeled in GaussView 03, and optimised using the HF/3-21G protocol. The optimised fragment was then reproduced twice and the fragments were orientated such that they imitated the chair transition state.

This transition state was then manually optimised using two alternative methods. The optimisations become difficult as in order to compute, it is necessary for the method to have "knowledge" of where the negative direction of curvature (the reaction coordinate) is. Providing a reasonable guess has been made, the easiest way to obtain the required information is to compute the force constant matrix in the initial step of an optimisation, which can be updated as the optimisation proceeds. In some cases it is possible to generate a more accurate transition structure by freezing the reaction coordinate. Once the molecule is fully relaxed, reaction coordinate constraints can be removed, followed by optimisation of the transition state.

====Optimisation to a TS (Berny)====

The approximated transition state structure was optimised using the HF/3-21G protocol. The Job Type was chosen as 'Opt+Freq' and the method was further modified by changing 'Optimization to a Minimum' to 'Optimization to a TS (Berny)'. Force constants were set to calculate only once.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:imaginaryfrequencycopeajm308.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Frozen Coordinate Method====

The optimisation was then carried out using the frozen coordinate method. The approximated transition state structure was again used. The method outlined @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was followed.

On completion of the submitted job, the output showed that the optimised structure was very similar to that found using the 'Optimisation to TS (Berny)' method, however it is noted that bond breaking/forming distances are fixed at 2.2 A. The constraints imposed before submitting the job were removed, and the transition state was optimised again.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:AJM308FrozenMethod.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Comparison====

The two methods concur.

Although the two methods were both successful in this case, there are advantages and disadvantages to both.

The 'Optimisation to TS (Berny)' method requires an accurate approximate transition state in order to yield accurate results. For the simple case above this was relatively easy, however, in more complex systems it may not be as simple.

Although the frozen coordinate method does not require as accurate an initial transition state as the 'Optimisation to TS (Berny)' method, it is more computationally expensive.

===Boat===

Another method was then used to optimise the boat transition state. The method utilised was the QST2 method. Reactants and products are specified for the reaction and a computational interpolation will attempt to locate the transition state.

Again, the method located @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was adhered to in order to prepare a Gaussian Input File.

The first QST2 calculation was then initiated. The Job Type was altered to 'Opt+Freq' and 'Optimise to a TS (QST2)'. This job was then submitted and failed. This failure highlights an inherent deficiency in the capability of computational chemistry. If the input file does not contain all the information required by the computational method, it will not succeed.

In order for the method to succeed the reactant and product geometries needed to be altered so that they more closely resemble the boat transition structure. The geometries were altered, with the central C-C-C-C dihedral angle being set to 0 o and the inside C-C-C angles set to 100 o.

The job was then resubmitted.

Only one imaginary vibrational frequency was returned, -840 cm-1 and the motion is shown below:

<center> [[Image:AJM308Boat.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.14 A.

The Energy of the transition state was found to be -231.60 a.u.

===Intrinsic Reaction Coordinate Method===

This method allows the following of the minimum energy path from the transition structure to its local minimum on the potential energy surface. A series of points is produced by taking small geometry steps in the direction of the steepest energy gradient. Initially it was chosen to run the method across 50 points on the potential energy surface, for both the chair and the boat transition states. The computation was run only in the forward direction due to the symmetry of the potential energy surface in this example. However, standard protocol is to run the method in both the forward and backward directions.

====Chair====

On opening the output file it was observed that no minimum had been reached in the computation.

Three options are then available:

1. Take the last point on the initial IRC and run a normal minimisation.

2. Restart the IRC and run with a larger number of points.

3. Specify that force constants should be computed at each step.

Approach 1 would be the least computationally costly, but the wrong minima may be found. Approach 2 is more reliable, but again, problems related to finding the wrong structure can present if too many points are required. Approach 3 is the most computationally expensive, but also the most reliable. It was decided to complete the IRC method using approached 1 and 3. The results for the chair transition state are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.62
|[[Image:ajm308chairirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.70
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.69
|[[Image:ajm308chairirc2.jpg|thumb|left|]]
|Minimum found.
|----
|}

</center>

Approach 1 yielded the lowest energy minima, with the method being far more efficient than Approach 3. The chair transition structure was shown to minimise to the 'Gauche 2' conformation.

====Boat====

The same methodology was applied to the Boat transition structure. Results are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.68
|[[Image:ajm308boatirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.68
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.65
|[[Image:ajm308boatirc2.jpg|thumb|left|]]
|Minimum not found.
|----
|}

</center>

===Further Analysis===

Both the Chair and Boat transition structures were reoptimised using the more advanced B3LYP/6-31G protocol, with frequency analysis also being performed. The two methods utilised are compared in the tables below:

<center>

{| border="1"
!colspan="3"|'''Chair'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G
|----
|Energy (a.u)
| -231.61
| -234.56
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (a.u)
| -231.60
| -234.54
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

</center>

Results show that the change to a more comprehensive method has little effect on the geometries of the transition states, as defined by bond angles, bond lengths and inter-fragment distances.

However, there is quite a marked difference between the total relative energy of the transition structures.

====Thermochemical Data====

'''Chair TS - HF/3-21G'''

A. -231.47 a.u

B. -231.46 a.u

C. -231.46 a.u

D. -231.50 a.u

'''Chair TS - B3LYP/6-31G'''

A. -234.41 a.u

B. -234.41 a.u

C. -234.41 a.u

D. -234.44 a.u

'''Boat TS - HF/3-21G'''

A. -231.45 a.u

B. -231.45 a.u

C. -231.44 a.u

D. -231.48 a.u

'''Boat TS - B3LYP/6-31G'''

A. -234.40 a.u

B. -234.40 a.u

C. -234.40 a.u

D. -234.43 a.u

{Where A,B,C and D are defined as earlier}

These values correlate well with those found @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]

Using these values it was possible to calculate activation energies, as shown in the table below:

<center>

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

</center>

Values calculated with the more advanced methodology are closer to experimental values than those calculated with the HF/3-21G level of theory.

The chair transition state has a lower activation energy than the boat transition state, in agreement with the literature <ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. This is on account of the reduced steric hindrance encountered proceeding via the chair transition state than the boat transition state.

=Diels Alder Cyclo-Addition=

The Diels-Alder cycloaddition occurs between a diene and a dienophile, with a wide range of molecules able to take on each role, and is an example of a pericyclic reaction. The reaction is only allowed (ie. not forbidden) if the HOMO of one reactant is able to interact with the LUMO of the other. There must be sufficient orbital overlap for the reaction to be allowed, and as such the symmetry properties of the orbitals in question must be identical.

A substituted dienophile can invoke secondary orbital effects, resulting in regioselectivity.

The simplest Diels-Alder reaction is that which occurs between ethene (the dienophile) and cis-butadiene (the diene).

<center> [[Image:Mb da3.jpg|thumb|center|]] </center>

Principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] as the diene, butadiene, has 4 π orbitals in its π system.

==Ethene and cis-Butadiene==

cis-Butadiene and ethene were modeled in GaussView 03, and optimised in Gaussian. The semi-empirical AM1 method was utilised and the molecular orbitals were visualised and are illustrated below:

Relative energy, and symmetry in relation to the σv plane are also indicated.

<center>

{| border="1"
!Molecule
!Total Energy of Molecule (a.u)
!HOMO energy (a.u)
!Visualised HOMO
!HOMO Symmetry (with respect to σv plane)
!LUMO Energy (a.u)
!Visualised LUMO
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.026
| -0.39
|[[Image:ajm308EtheneHOMO.jpg|thumb|]]
|Symmetric
|0.052
|[[Image:ajm308EtheneLUMO.jpg|thumb|]]
|Antisymmetric
|----
|Cis-butadiene
|0.049
| -0.34
|[[Image:ajm308CBHOMO.jpg|thumb|]]
|Antisymmetric
|0.017
|[[Image:ajm308CBLUMO.jpg|thumb|]]
|Symmetric
|----
|}

</center>

Only orbitals of identical symmetry have the required overlap density for the reaction to proceed, and so it can be seen that the HOMO of cis-butadiene can interact with the LUMO of ethene, and vice versa.

===Transition States===

The overlap between the two sets of pi orbitals is maximised by adopting an envelope type structure. In order to obtain the starting geometry a bicyclic system was modeled, and the -CH2-CH2- fragment removed. Inter-fragment distance was then guessed to be 2.15 A.

Optimisation was then carried out, using methodology similar to that found in Section xxx above.

One imaginary frequency was found to be -818 cm-1. This vibration is visualised below and shows synchronous bond forming, concurring with the concerted nature of pericyclic reactions.

<center>

[[Image:DAvibsajm308.gif]]

</center>

The lowest real vibrational frequency is observed at 167 cm-1 and is attributed to the rocking of the CH2=CH2 section of the transition structure.

The energy of the transition structure was found to be -231.60 a.u.

The HOMO and LUMO of the transition state were also visualised and are shown below:

<center>

[[Image:HOMODAajm308.jpg|thumb|center|]]

[[Image:LUMODAajm308.jpg|thumb|center|]]

</center>

The HOMO is antisymmetric, and can be associated with overlap of the HOMO of cis-butadiene and the LUMO of ethene - where two antisymmetric molecular orbitals overlap.

Similarly, the LUMO is symmetric, and can be associated with overlap of the LUMO of cis-butadiene and the HOMO of ethene.

The geometry of the transition structure is outlined in the table below.

<center>

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C Length
| -
|2.21 A
|----
|Ethene C=C Length
|1.33 A
|1.38 A
|----
|Butadiene C=C Length
|1.34 A
|1.37 A
|----
|Butadiene C-C Length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C Angle
|125.6°
|121.5°
|----
|}

</center>

The C-C, that is only partially formed in the transition state, is markedly longer than any other bond present as a result of this. C-C and C=C bonds are no longer differentiable in the transition state, as they are in the reactants. Typical sp3 C-C bond lengths of 1.54 A <ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref> correlate well with the calculated C-C bond distance in butadiene. Calculated sp2 C=C bond lengths of 1.34 A and 1.33 A correlate very well with the typical values.

The Van der Waal's radius of the C atom is 1.7 A. <ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

==Cyclohexa-1,3-diene with Maleic Anhydride==

The reaction of cyclohexa-1,3-diene and maleic anhydride yields the endo product in majority. The reaction proceeds under kinetic control so it assumed that the exo transition state is at higher energy.

[[Image:Ajm308reactionscheme.gif|center|]]

===Transition States===

Again, bicyclic systems were used in order to model the transition states for both the endo and exo products. 2.2 A was used as an initial guess for the inter-fragment distances, and both structures were optimised using the 'Optimisation to TS (Berny)' method, as outlined in section xxx above.

Frequency analysis was also performed.

Geometric and thermochemical properties, as well as the imaginary vibrational motions returned are displayed in the table below:

<center>

{| border="1"
|Property
|Exo
|Endo
|----
|Product Energy (a.u)
| -0.16
| -0.16
|----
|Transition State Energy (a.u)
| -0.051
| -0.052
|----
|Imaginary Vibrational Frequency (cm-1)
| -812
| -806
|----
|Imaginary Vibration Animation
|[[Image:EXOVibajm308.gif|thumb|left|350px|]]
|[[Image:ENDOVIBajm308.gif|thumb|left|350px|]]
|----
|Lowest Real Frequency (cm-1)
|61
|62
|----
|Lowest Real Frequency Assignment
|Rocking of Cyclohexadiene Fragment
|Rocking of Cyclohexadiene Fragment
|----
|Fragment Bond Distance (A)
|2.17
|2.16
|----
|(C=O)-C-(C=O) Through Space Distance (A)
|2.28
|2.28
|----
|C=C Distance (A)
|1.40
|1.40
|----
|C-C Bridge Distance (A)
|1.52
|1.52
|----
|HOMO
|[[Image:EXOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|LUMO
|[[Image:EXOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|}

</center>

The thermochemical properties are in agreement with the prediction that the endo product will be major, the exo minor. The endo transition state has a lower transition state than the exo transition state, and as the reaction is under kinetic control, is favoured as the reaction energy barrier is smaller.

The HOMOs visualised above show differences between the endo and exo transition states, in the -(C=O)-O-(C=O)- region. The endo transition state has appreciable electron density in the region, however, the exo transition state does not. There is clearly more secondary orbital effects operating in the endo transition state, than in the exo transition state. The transition state is stabilised by these interactions, thus lowering the energy of the endo transition state relative to the exo transition state. This secondary orbital interaction is shown in the diagram below:

!!!Diagram!!!

=Conclusions=

Once again, the power of computational chemistry is apparent, as is the need to balance the desired accuracy of the calculations against computational cost and time constraints. One example is when using the QST2 method which is more efficient than the QST3 method, but has the potential to fail if reactants and products are not close to the transition structure. It seems it is often worth utilising a lower level protocol initially, and if the desired results are not obtained, then a higher level calculation should be carried out.

The wide range of information gleaned from the computational methods, and close correlation with experimental results, means computational chemistry rightly deserves a place alongside more traditional methods of experimentation.

Limitations of the field are also apparent in accounting for more complex physical phenomena, such as solvent effects.

=References=

<references/>

Rep:Mod:ajm3081989

2011-02-18T12:25:07Z

Ajm308: /* Transition States */

James Marks ( ajm308 / 00548888 ) - {10/02/2011 - 18/02/2011}

=Introduction=

Computations will be carried out in order to characterise the transition states involved in both the Cope rearrangement and the Diels-Alder cycloaddition reactions.

Force field and molecular mechanics methods used in previous experiments are unsuitable for characterising transition states as they are unable to adequately describe the processes of bond making and bond breaking, as well as change in bonding type and electron distribution.

Molecular orbital based methods must be used instead, which involve solving the Schrodinger equation numerically.

Reaction pathways and barrier heights can also be calculated, along with the structures of transitions states.

__TOC__

=Cope Rearrangement=

The Cope rearrangement is an example of a [3,3]-sigmatropic shift rearrangement.

<center> [[Image:ajm308coperearrangement.gif]] </center>

The Cope rearrangement of 1,5-hexadiene will be used as an example, to aid understanding of methods used in investigating chemical reactivity computationally.

The objective is to locate the low energy minima, as well as transition structures on the potential energy surface, in order to determine the preferred reaction mechanism.

It has previously been deduced, both experimentally and computationally, that the reaction proceeds in a concerted fashion via either one of two transition states - the 'chair' or the 'boat':

[[Image:chairconfajm308.png|thumb|center|Chair|]]

[[Image:ajm308boat.png|thumb|center|Boat|]]

==Optimising Reactants and Products==

There a number of possible conformations of 1,5-hexadiene, with each having a distinct total energy.

Initially, 1,5-hexadiene was modeled in GaussView 03 with an 'anti' conformation. This structure was then optimised using the HF/3-21G method and basis set. The optimisation calculation was submitted to Gaussian. Having opened the output files in GaussView 03, the optimised structures were 'symmetrised' in order to determine point group.

The same method was followed on an initially 'gauche' conformation of 1,5-hexadiene. It was anticipated that the 'gauche' conformer would have a higher relative total energy than the 'anti' conformer, on account of the reduced steric repulsion in the arrangement. Initially this assumption was thought to be correct, as the optimised 'gauche' conformer did indeed have a higher relative total energy than the 'anti' conformer. On further investigation, the low energy conformer of 1,5-hexadiene was found to be a 'gauche' example. The lower relative total energy of this conformation can be accounted for by considering the possibility that favourable Van der Waal's interactions between hydrogen atoms are able to override the intrinsic steric strain within the conformation.

As the "anti 2" conformer was not located during initial optimisation, the conformer was modeled in GaussView 03, and optimised to yield the Ci symmetric 'anti' conformer. It was first optimised using the same HF/3-21G protocol, followed by further optimisation with the B3LYP/6-31G protocol. This second protocol is a more computationally intensive optimisation with a larger basis set, and thus could be expected to produce more accurate results.

A summary of the results and characteristics of all aforementioned calculations and conformers is included in the table below:

<center>

{| border="1"
!Conformation
!Theory level
!Computed energy (a.u)
!Appendix Value (a.u)
!Symmetry Point Group
!Structure
!Conformer
|----
|Anti
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 1
|----
|Gauche
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 2
|----
|Lowest Energy Conformer
|HF/3-21G
| -231.69
| -231.69
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 3
|----
|Ci Anti 2 conformation
|HF/3-21G
| -231.69
| -231.69
|Ci
|
|Anti 2
|----
|Ci Anti 2 conformation
|B3LYP/6-31G
| -234.61
| -234.61
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 2
|----
|}

</center>

The two levels of theory, the more advanced B3LYP/6-31G and the more simple HF/3-21G, both returned optimised geometries that are superficially very similar. The difference in relative total energies of the two optimised "Anti 2" conformers was found to be 2.919 a.u.

Closer analysis of the optimised geometries was able to highlight slight differences between the two.

Dihedral angles were compared, as well as bond lengths.

<center>

{| border="1"
!Atoms & Measurement
!HF/3-21G
!B3LYP/6-31G
!Difference
|----
|1,2,3,4 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2,3,4,5 Dihedral angle
|180.0°
|180.0°
|0°
|----
|3,4,5,6 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|1,2 Bond length
|1.316 A
|1.334 A
|0.018 A
|----
|2,3 Bond length
|1.509 A
|1.504 A
|0.005 A
|----
|3,4 Bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

</center>

The more advanced protocol gives dihedral angles and bond lengths which differ from the less advanced protocol, but only to a slight extent, with bond lengths proving more reliable at the HF/3-21G level than the dihedral angles.

===Frequency Calculations===

The B3LYP/6-31G optimised was then submitted to frequency calculations.

Frequency calculations, as shown in previous modules, are able to confirm that a minimum has been reached, by showing that all vibrational frequencies are positive and real.

Following frequency calculations at the same level of theory, the vibrational frequencies were all confirmed to be positive and real, with the computed IR Spectra shown below:

<center> [[Image:AJMIRSpectra.jpg]] </center>

The output file was then used to find Thermochemical data. Four pieces of important data were noted.

A = The potential energy at 0 K, including zero-point vibrational energy. (E = Eelec + ZPE)

B = The energy at 298.15 K, 1 atm, including contributions from Translation, Rotational and Vibrational energy modes. (E = E + Evib + Erot + Etrans)

C = A correction for RT. (H = E + RT)

D = Includes the entropic contribution to free energy. (G = H - TS)

A. Sum of Electronic and Zero Point Energies: -234.47 a.u

B. Sum of Electronic and Thermal Energies: -234.46 a.u

C. Sum of Electronic and Thermal Enthalpies: -234.46 a.u

D. Sum of Electronic and Thermal Free Energies: -234.50 a.u

==Chair and Boat Transition Structures==

===Chair===

Initially an allyl (CH2CHCH2) fragment was modeled in GaussView 03, and optimised using the HF/3-21G protocol. The optimised fragment was then reproduced twice and the fragments were orientated such that they imitated the chair transition state.

This transition state was then manually optimised using two alternative methods. The optimisations become difficult as in order to compute, it is necessary for the method to have "knowledge" of where the negative direction of curvature (the reaction coordinate) is. Providing a reasonable guess has been made, the easiest way to obtain the required information is to compute the force constant matrix in the initial step of an optimisation, which can be updated as the optimisation proceeds. In some cases it is possible to generate a more accurate transition structure by freezing the reaction coordinate. Once the molecule is fully relaxed, reaction coordinate constraints can be removed, followed by optimisation of the transition state.

====Optimisation to a TS (Berny)====

The approximated transition state structure was optimised using the HF/3-21G protocol. The Job Type was chosen as 'Opt+Freq' and the method was further modified by changing 'Optimization to a Minimum' to 'Optimization to a TS (Berny)'. Force constants were set to calculate only once.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:imaginaryfrequencycopeajm308.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Frozen Coordinate Method====

The optimisation was then carried out using the frozen coordinate method. The approximated transition state structure was again used. The method outlined @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was followed.

On completion of the submitted job, the output showed that the optimised structure was very similar to that found using the 'Optimisation to TS (Berny)' method, however it is noted that bond breaking/forming distances are fixed at 2.2 A. The constraints imposed before submitting the job were removed, and the transition state was optimised again.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:AJM308FrozenMethod.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Comparison====

The two methods concur.

Although the two methods were both successful in this case, there are advantages and disadvantages to both.

The 'Optimisation to TS (Berny)' method requires an accurate approximate transition state in order to yield accurate results. For the simple case above this was relatively easy, however, in more complex systems it may not be as simple.

Although the frozen coordinate method does not require as accurate an initial transition state as the 'Optimisation to TS (Berny)' method, it is more computationally expensive.

===Boat===

Another method was then used to optimise the boat transition state. The method utilised was the QST2 method. Reactants and products are specified for the reaction and a computational interpolation will attempt to locate the transition state.

Again, the method located @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was adhered to in order to prepare a Gaussian Input File.

The first QST2 calculation was then initiated. The Job Type was altered to 'Opt+Freq' and 'Optimise to a TS (QST2)'. This job was then submitted and failed. This failure highlights an inherent deficiency in the capability of computational chemistry. If the input file does not contain all the information required by the computational method, it will not succeed.

In order for the method to succeed the reactant and product geometries needed to be altered so that they more closely resemble the boat transition structure. The geometries were altered, with the central C-C-C-C dihedral angle being set to 0 o and the inside C-C-C angles set to 100 o.

The job was then resubmitted.

Only one imaginary vibrational frequency was returned, -840 cm-1 and the motion is shown below:

<center> [[Image:AJM308Boat.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.14 A.

The Energy of the transition state was found to be -231.60 a.u.

===Intrinsic Reaction Coordinate Method===

This method allows the following of the minimum energy path from the transition structure to its local minimum on the potential energy surface. A series of points is produced by taking small geometry steps in the direction of the steepest energy gradient. Initially it was chosen to run the method across 50 points on the potential energy surface, for both the chair and the boat transition states. The computation was run only in the forward direction due to the symmetry of the potential energy surface in this example. However, standard protocol is to run the method in both the forward and backward directions.

====Chair====

On opening the output file it was observed that no minimum had been reached in the computation.

Three options are then available:

1. Take the last point on the initial IRC and run a normal minimisation.

2. Restart the IRC and run with a larger number of points.

3. Specify that force constants should be computed at each step.

Approach 1 would be the least computationally costly, but the wrong minima may be found. Approach 2 is more reliable, but again, problems related to finding the wrong structure can present if too many points are required. Approach 3 is the most computationally expensive, but also the most reliable. It was decided to complete the IRC method using approached 1 and 3. The results for the chair transition state are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.62
|[[Image:ajm308chairirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.70
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.69
|[[Image:ajm308chairirc2.jpg|thumb|left|]]
|Minimum found.
|----
|}

</center>

Approach 1 yielded the lowest energy minima, with the method being far more efficient than Approach 3. The chair transition structure was shown to minimise to the 'Gauche 2' conformation.

====Boat====

The same methodology was applied to the Boat transition structure. Results are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.68
|[[Image:ajm308boatirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.68
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.65
|[[Image:ajm308boatirc2.jpg|thumb|left|]]
|Minimum not found.
|----
|}

</center>

===Further Analysis===

Both the Chair and Boat transition structures were reoptimised using the more advanced B3LYP/6-31G protocol, with frequency analysis also being performed. The two methods utilised are compared in the tables below:

<center>

{| border="1"
!colspan="3"|'''Chair'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G
|----
|Energy (a.u)
| -231.61
| -234.56
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (a.u)
| -231.60
| -234.54
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

</center>

Results show that the change to a more comprehensive method has little effect on the geometries of the transition states, as defined by bond angles, bond lengths and inter-fragment distances.

However, there is quite a marked difference between the total relative energy of the transition structures.

====Thermochemical Data====

'''Chair TS - HF/3-21G'''

A. -231.47 a.u

B. -231.46 a.u

C. -231.46 a.u

D. -231.50 a.u

'''Chair TS - B3LYP/6-31G'''

A. -234.41 a.u

B. -234.41 a.u

C. -234.41 a.u

D. -234.44 a.u

'''Boat TS - HF/3-21G'''

A. -231.45 a.u

B. -231.45 a.u

C. -231.44 a.u

D. -231.48 a.u

'''Boat TS - B3LYP/6-31G'''

A. -234.40 a.u

B. -234.40 a.u

C. -234.40 a.u

D. -234.43 a.u

{Where A,B,C and D are defined as earlier}

These values correlate well with those found @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]

Using these values it was possible to calculate activation energies, as shown in the table below:

<center>

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

</center>

Values calculated with the more advanced methodology are closer to experimental values than those calculated with the HF/3-21G level of theory.

The chair transition state has a lower activation energy than the boat transition state, in agreement with the literature <ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. This is on account of the reduced steric hindrance encountered proceeding via the chair transition state than the boat transition state.

=Diels Alder Cyclo-Addition=

The Diels-Alder cycloaddition occurs between a diene and a dienophile, with a wide range of molecules able to take on each role, and is an example of a pericyclic reaction. The reaction is only allowed (ie. not forbidden) if the HOMO of one reactant is able to interact with the LUMO of the other. There must be sufficient orbital overlap for the reaction to be allowed, and as such the symmetry properties of the orbitals in question must be identical.

A substituted dienophile can invoke secondary orbital effects, resulting in regioselectivity.

The simplest Diels-Alder reaction is that which occurs between ethene (the dienophile) and cis-butadiene (the diene).

<center> [[Image:Mb da3.jpg|thumb|center|]] </center>

Principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] as the diene, butadiene, has 4 π orbitals in its π system.

==Ethene and cis-Butadiene==

cis-Butadiene and ethene were modeled in GaussView 03, and optimised in Gaussian. The semi-empirical AM1 method was utilised and the molecular orbitals were visualised and are illustrated below:

Relative energy, and symmetry in relation to the σv plane are also indicated.

<center>

{| border="1"
!Molecule
!Total Energy of Molecule (a.u)
!HOMO energy (a.u)
!Visualised HOMO
!HOMO Symmetry (with respect to σv plane)
!LUMO Energy (a.u)
!Visualised LUMO
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.026
| -0.39
|[[Image:ajm308EtheneHOMO.jpg|thumb|]]
|Symmetric
|0.052
|[[Image:ajm308EtheneLUMO.jpg|thumb|]]
|Antisymmetric
|----
|Cis-butadiene
|0.049
| -0.34
|[[Image:ajm308CBHOMO.jpg|thumb|]]
|Antisymmetric
|0.017
|[[Image:ajm308CBLUMO.jpg|thumb|]]
|Symmetric
|----
|}

</center>

Only orbitals of identical symmetry have the required overlap density for the reaction to proceed, and so it can be seen that the HOMO of cis-butadiene can interact with the LUMO of ethene, and vice versa.

===Transition States===

The overlap between the two sets of pi orbitals is maximised by adopting an envelope type structure. In order to obtain the starting geometry a bicyclic system was modeled, and the -CH2-CH2- fragment removed. Inter-fragment distance was then guessed to be 2.15 A.

Optimisation was then carried out, using methodology similar to that found in Section xxx above.

One imaginary frequency was found to be -818 cm-1. This vibration is visualised below and shows synchronous bond forming, concurring with the concerted nature of pericyclic reactions.

<center>

[[Image:DAvibsajm308.gif]]

</center>

The lowest real vibrational frequency is observed at 167 cm-1 and is attributed to the rocking of the CH2=CH2 section of the transition structure.

The energy of the transition structure was found to be -231.60 a.u.

The HOMO and LUMO of the transition state were also visualised and are shown below:

<center>

[[Image:HOMODAajm308.jpg|thumb|center|]]

[[Image:LUMODAajm308.jpg|thumb|center|]]

</center>

The HOMO is antisymmetric, and can be associated with overlap of the HOMO of cis-butadiene and the LUMO of ethene - where two antisymmetric molecular orbitals overlap.

Similarly, the LUMO is symmetric, and can be associated with overlap of the LUMO of cis-butadiene and the HOMO of ethene.

The geometry of the transition structure is outlined in the table below.

<center>

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C Length
| -
|2.21 A
|----
|Ethene C=C Length
|1.33 A
|1.38 A
|----
|Butadiene C=C Length
|1.34 A
|1.37 A
|----
|Butadiene C-C Length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C Angle
|125.6°
|121.5°
|----
|}

</center>

The C-C, that is only partially formed in the transition state, is markedly longer than any other bond present as a result of this. C-C and C=C bonds are no longer differentiable in the transition state, as they are in the reactants. Typical sp3 C-C bond lengths of 1.54 A <ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref> correlate well with the calculated C-C bond distance in butadiene. Calculated sp2 C=C bond lengths of 1.34 A and 1.33 A correlate very well with the typical values.

The Van der Waal's radius of the C atom is 1.7 A. <ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

==Cyclohexa-1,3-diene with Maleic Anhydride==

The reaction of cyclohexa-1,3-diene and maleic anhydride yields the endo product in majority. The reaction proceeds under kinetic control so it assumed that the exo transition state is at higher energy.

[[Image:Ajm308reactionscheme.gif|center|]]

===Transition States===

Again, bicyclic systems were used in order to model the transition states for both the endo and exo products. 2.2 A was used as an initial guess for the inter-fragment distances, and both structures were optimised using the 'Optimisation to TS (Berny)' method, as outlined in section xxx above.

Frequency analysis was also performed.

Geometric and thermochemical properties, as well as the imaginary vibrational motions returned are displayed in the table below:

<center>

{| border="1"
|Property
|Exo
|Endo
|----
|Product Energy (a.u)
| -0.16
| -0.16
|----
|Transition State Energy (a.u)
| -0.051
| -0.052
|----
|Imaginary Vibrational Frequency (cm-1)
| -812
| -806
|----
|Imaginary Vibration Animation
|[[Image:EXOVIBajm308.gif|thumb|left|350px|]]
|[[Image:ENDOVIBajm308.gif|thumb|left|350px|]]
|----
|Lowest Real Frequency (cm-1)
|61
|62
|----
|Lowest Real Frequency Assignment
|Rocking of Cyclohexadiene Fragment
|Rocking of Cyclohexadiene Fragment
|----
|Fragment Bond Distance (A)
|2.17
|2.16
|----
|(C=O)-C-(C=O) Through Space Distance (A)
|2.28
|2.28
|----
|C=C Distance (A)
|1.40
|1.40
|----
|C-C Bridge Distance (A)
|1.52
|1.52
|----
|HOMO
|[[Image:EXOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOHOMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|LUMO
|[[Image:EXOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|[[Image:ENDOLUMOajm308.jpg|thumb|left|350px|]]

Antisymmetric
|----
|}

</center>

The thermochemical properties are in agreement with the prediction that the endo product will be major, the exo minor. The endo transition state has a lower transition state than the exo transition state, and as the reaction is under kinetic control, is favoured as the reaction energy barrier is smaller.

The HOMOs visualised above show differences between the endo and exo transition states, in the -(C=O)-O-(C=O)- region. The endo transition state has appreciable electron density in the region, however, the exo transition state does not. There is clearly more secondary orbital effects operating in the endo transition state, than in the exo transition state. The transition state is stabilised by these interactions, thus lowering the energy of the endo transition state relative to the exo transition state. This secondary orbital interaction is shown in the diagram below:

!!!Diagram!!!

=Conclusions=

Once again, the power of computational chemistry is apparent, as is the need to balance the desired accuracy of the calculations against computational cost and time constraints. One example is when using the QST2 method which is more efficient than the QST3 method, but has the potential to fail if reactants and products are not close to the transition structure. It seems it is often worth utilising a lower level protocol initially, and if the desired results are not obtained, then a higher level calculation should be carried out.

The wide range of information gleaned from the computational methods, and close correlation with experimental results, means computational chemistry rightly deserves a place alongside more traditional methods of experimentation.

Limitations of the field are also apparent in accounting for more complex physical phenomena, such as solvent effects.

=References=

<references/>

File:EXOVIbajm308.gif

2011-02-18T12:24:51Z

Ajm308:

File:ENDOVIBajm308.gif

2011-02-18T12:24:28Z

Ajm308:

File:EXOVIBajm308.jpg

2011-02-18T12:22:47Z

Ajm308:

Rep:Mod:ajm3081989

2011-02-18T12:22:02Z

Rep:Mod:ajm3081989

2011-02-18T12:18:31Z

Ajm308: /* Transition States */

James Marks ( ajm308 / 00548888 ) - {10/02/2011 - 18/02/2011}

=Introduction=

Computations will be carried out in order to characterise the transition states involved in both the Cope rearrangement and the Diels-Alder cycloaddition reactions.

Force field and molecular mechanics methods used in previous experiments are unsuitable for characterising transition states as they are unable to adequately describe the processes of bond making and bond breaking, as well as change in bonding type and electron distribution.

Molecular orbital based methods must be used instead, which involve solving the Schrodinger equation numerically.

Reaction pathways and barrier heights can also be calculated, along with the structures of transitions states.

__TOC__

=Cope Rearrangement=

The Cope rearrangement is an example of a [3,3]-sigmatropic shift rearrangement.

<center> [[Image:ajm308coperearrangement.gif]] </center>

The Cope rearrangement of 1,5-hexadiene will be used as an example, to aid understanding of methods used in investigating chemical reactivity computationally.

The objective is to locate the low energy minima, as well as transition structures on the potential energy surface, in order to determine the preferred reaction mechanism.

It has previously been deduced, both experimentally and computationally, that the reaction proceeds in a concerted fashion via either one of two transition states - the 'chair' or the 'boat':

[[Image:chairconfajm308.png|thumb|center|Chair|]]

[[Image:ajm308boat.png|thumb|center|Boat|]]

==Optimising Reactants and Products==

There a number of possible conformations of 1,5-hexadiene, with each having a distinct total energy.

Initially, 1,5-hexadiene was modeled in GaussView 03 with an 'anti' conformation. This structure was then optimised using the HF/3-21G method and basis set. The optimisation calculation was submitted to Gaussian. Having opened the output files in GaussView 03, the optimised structures were 'symmetrised' in order to determine point group.

The same method was followed on an initially 'gauche' conformation of 1,5-hexadiene. It was anticipated that the 'gauche' conformer would have a higher relative total energy than the 'anti' conformer, on account of the reduced steric repulsion in the arrangement. Initially this assumption was thought to be correct, as the optimised 'gauche' conformer did indeed have a higher relative total energy than the 'anti' conformer. On further investigation, the low energy conformer of 1,5-hexadiene was found to be a 'gauche' example. The lower relative total energy of this conformation can be accounted for by considering the possibility that favourable Van der Waal's interactions between hydrogen atoms are able to override the intrinsic steric strain within the conformation.

As the "anti 2" conformer was not located during initial optimisation, the conformer was modeled in GaussView 03, and optimised to yield the Ci symmetric 'anti' conformer. It was first optimised using the same HF/3-21G protocol, followed by further optimisation with the B3LYP/6-31G protocol. This second protocol is a more computationally intensive optimisation with a larger basis set, and thus could be expected to produce more accurate results.

A summary of the results and characteristics of all aforementioned calculations and conformers is included in the table below:

<center>

{| border="1"
!Conformation
!Theory level
!Computed energy (a.u)
!Appendix Value (a.u)
!Symmetry Point Group
!Structure
!Conformer
|----
|Anti
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 1
|----
|Gauche
|HF/3-21G
| -231.69
| -231.69
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 2
|----
|Lowest Energy Conformer
|HF/3-21G
| -231.69
| -231.69
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Gauche 3
|----
|Ci Anti 2 conformation
|HF/3-21G
| -231.69
| -231.69
|Ci
|
|Anti 2
|----
|Ci Anti 2 conformation
|B3LYP/6-31G
| -234.61
| -234.61
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|Anti 2
|----
|}

</center>

The two levels of theory, the more advanced B3LYP/6-31G and the more simple HF/3-21G, both returned optimised geometries that are superficially very similar. The difference in relative total energies of the two optimised "Anti 2" conformers was found to be 2.919 a.u.

Closer analysis of the optimised geometries was able to highlight slight differences between the two.

Dihedral angles were compared, as well as bond lengths.

<center>

{| border="1"
!Atoms & Measurement
!HF/3-21G
!B3LYP/6-31G
!Difference
|----
|1,2,3,4 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2,3,4,5 Dihedral angle
|180.0°
|180.0°
|0°
|----
|3,4,5,6 Dihedral angle
|114.626°
|118.53°
|3.904°
|----
|1,2 Bond length
|1.316 A
|1.334 A
|0.018 A
|----
|2,3 Bond length
|1.509 A
|1.504 A
|0.005 A
|----
|3,4 Bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

</center>

The more advanced protocol gives dihedral angles and bond lengths which differ from the less advanced protocol, but only to a slight extent, with bond lengths proving more reliable at the HF/3-21G level than the dihedral angles.

===Frequency Calculations===

The B3LYP/6-31G optimised was then submitted to frequency calculations.

Frequency calculations, as shown in previous modules, are able to confirm that a minimum has been reached, by showing that all vibrational frequencies are positive and real.

Following frequency calculations at the same level of theory, the vibrational frequencies were all confirmed to be positive and real, with the computed IR Spectra shown below:

<center> [[Image:AJMIRSpectra.jpg]] </center>

The output file was then used to find Thermochemical data. Four pieces of important data were noted.

A = The potential energy at 0 K, including zero-point vibrational energy. (E = Eelec + ZPE)

B = The energy at 298.15 K, 1 atm, including contributions from Translation, Rotational and Vibrational energy modes. (E = E + Evib + Erot + Etrans)

C = A correction for RT. (H = E + RT)

D = Includes the entropic contribution to free energy. (G = H - TS)

A. Sum of Electronic and Zero Point Energies: -234.47 a.u

B. Sum of Electronic and Thermal Energies: -234.46 a.u

C. Sum of Electronic and Thermal Enthalpies: -234.46 a.u

D. Sum of Electronic and Thermal Free Energies: -234.50 a.u

==Chair and Boat Transition Structures==

===Chair===

Initially an allyl (CH2CHCH2) fragment was modeled in GaussView 03, and optimised using the HF/3-21G protocol. The optimised fragment was then reproduced twice and the fragments were orientated such that they imitated the chair transition state.

This transition state was then manually optimised using two alternative methods. The optimisations become difficult as in order to compute, it is necessary for the method to have "knowledge" of where the negative direction of curvature (the reaction coordinate) is. Providing a reasonable guess has been made, the easiest way to obtain the required information is to compute the force constant matrix in the initial step of an optimisation, which can be updated as the optimisation proceeds. In some cases it is possible to generate a more accurate transition structure by freezing the reaction coordinate. Once the molecule is fully relaxed, reaction coordinate constraints can be removed, followed by optimisation of the transition state.

====Optimisation to a TS (Berny)====

The approximated transition state structure was optimised using the HF/3-21G protocol. The Job Type was chosen as 'Opt+Freq' and the method was further modified by changing 'Optimization to a Minimum' to 'Optimization to a TS (Berny)'. Force constants were set to calculate only once.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:imaginaryfrequencycopeajm308.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Frozen Coordinate Method====

The optimisation was then carried out using the frozen coordinate method. The approximated transition state structure was again used. The method outlined @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was followed.

On completion of the submitted job, the output showed that the optimised structure was very similar to that found using the 'Optimisation to TS (Berny)' method, however it is noted that bond breaking/forming distances are fixed at 2.2 A. The constraints imposed before submitting the job were removed, and the transition state was optimised again.

The calculation gave an imaginary frequency of -818 cm-1 as shown below:

<center> [[Image:AJM308FrozenMethod.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.02 A.

The Energy of the transition state was found to be -231.62 a.u.

====Comparison====

The two methods concur.

Although the two methods were both successful in this case, there are advantages and disadvantages to both.

The 'Optimisation to TS (Berny)' method requires an accurate approximate transition state in order to yield accurate results. For the simple case above this was relatively easy, however, in more complex systems it may not be as simple.

Although the frozen coordinate method does not require as accurate an initial transition state as the 'Optimisation to TS (Berny)' method, it is more computationally expensive.

===Boat===

Another method was then used to optimise the boat transition state. The method utilised was the QST2 method. Reactants and products are specified for the reaction and a computational interpolation will attempt to locate the transition state.

Again, the method located @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3] was adhered to in order to prepare a Gaussian Input File.

The first QST2 calculation was then initiated. The Job Type was altered to 'Opt+Freq' and 'Optimise to a TS (QST2)'. This job was then submitted and failed. This failure highlights an inherent deficiency in the capability of computational chemistry. If the input file does not contain all the information required by the computational method, it will not succeed.

In order for the method to succeed the reactant and product geometries needed to be altered so that they more closely resemble the boat transition structure. The geometries were altered, with the central C-C-C-C dihedral angle being set to 0 o and the inside C-C-C angles set to 100 o.

The job was then resubmitted.

Only one imaginary vibrational frequency was returned, -840 cm-1 and the motion is shown below:

<center> [[Image:AJM308Boat.gif]] </center>

The optimised distance between terminals of the allyl fragments was found to be 2.14 A.

The Energy of the transition state was found to be -231.60 a.u.

===Intrinsic Reaction Coordinate Method===

This method allows the following of the minimum energy path from the transition structure to its local minimum on the potential energy surface. A series of points is produced by taking small geometry steps in the direction of the steepest energy gradient. Initially it was chosen to run the method across 50 points on the potential energy surface, for both the chair and the boat transition states. The computation was run only in the forward direction due to the symmetry of the potential energy surface in this example. However, standard protocol is to run the method in both the forward and backward directions.

====Chair====

On opening the output file it was observed that no minimum had been reached in the computation.

Three options are then available:

1. Take the last point on the initial IRC and run a normal minimisation.

2. Restart the IRC and run with a larger number of points.

3. Specify that force constants should be computed at each step.

Approach 1 would be the least computationally costly, but the wrong minima may be found. Approach 2 is more reliable, but again, problems related to finding the wrong structure can present if too many points are required. Approach 3 is the most computationally expensive, but also the most reliable. It was decided to complete the IRC method using approached 1 and 3. The results for the chair transition state are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.62
|[[Image:ajm308chairirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.70
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.69
|[[Image:ajm308chairirc2.jpg|thumb|left|]]
|Minimum found.
|----
|}

</center>

Approach 1 yielded the lowest energy minima, with the method being far more efficient than Approach 3. The chair transition structure was shown to minimise to the 'Gauche 2' conformation.

====Boat====

The same methodology was applied to the Boat transition structure. Results are shown in the table below:

<center>

{| border="1"
!Type
!Energy (a.u)
!Energy Surface
!Notes
|----
|Initial IRC (50 steps)
| -231.68
|[[Image:ajm308boatirc.jpg|thumb|left|]]
|Minimum was not found. 50 steps not adequate.
|----
|Optimisation on Structure from Initial IRC
| -231.68
|
|Minimum found.
|----
|Force Constant computed at each iteration.
| -231.65
|[[Image:ajm308boatirc2.jpg|thumb|left|]]
|Minimum not found.
|----
|}

</center>

===Further Analysis===

Both the Chair and Boat transition structures were reoptimised using the more advanced B3LYP/6-31G protocol, with frequency analysis also being performed. The two methods utilised are compared in the tables below:

<center>

{| border="1"
!colspan="3"|'''Chair'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G
|----
|Energy (a.u)
| -231.61
| -234.56
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (a.u)
| -231.60
| -234.54
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

</center>

Results show that the change to a more comprehensive method has little effect on the geometries of the transition states, as defined by bond angles, bond lengths and inter-fragment distances.

However, there is quite a marked difference between the total relative energy of the transition structures.

====Thermochemical Data====

'''Chair TS - HF/3-21G'''

A. -231.47 a.u

B. -231.46 a.u

C. -231.46 a.u

D. -231.50 a.u

'''Chair TS - B3LYP/6-31G'''

A. -234.41 a.u

B. -234.41 a.u

C. -234.41 a.u

D. -234.44 a.u

'''Boat TS - HF/3-21G'''

A. -231.45 a.u

B. -231.45 a.u

C. -231.44 a.u

D. -231.48 a.u

'''Boat TS - B3LYP/6-31G'''

A. -234.40 a.u

B. -234.40 a.u

C. -234.40 a.u

D. -234.43 a.u

{Where A,B,C and D are defined as earlier}

These values correlate well with those found @ [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]

Using these values it was possible to calculate activation energies, as shown in the table below:

<center>

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

</center>

Values calculated with the more advanced methodology are closer to experimental values than those calculated with the HF/3-21G level of theory.

The chair transition state has a lower activation energy than the boat transition state, in agreement with the literature <ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. This is on account of the reduced steric hindrance encountered proceeding via the chair transition state than the boat transition state.

=Diels Alder Cyclo-Addition=

The Diels-Alder cycloaddition occurs between a diene and a dienophile, with a wide range of molecules able to take on each role, and is an example of a pericyclic reaction. The reaction is only allowed (ie. not forbidden) if the HOMO of one reactant is able to interact with the LUMO of the other. There must be sufficient orbital overlap for the reaction to be allowed, and as such the symmetry properties of the orbitals in question must be identical.

A substituted dienophile can invoke secondary orbital effects, resulting in regioselectivity.

The simplest Diels-Alder reaction is that which occurs between ethene (the dienophile) and cis-butadiene (the diene).

<center> [[Image:Mb da3.jpg|thumb|center|]] </center>

Principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] as the diene, butadiene, has 4 π orbitals in its π system.

==Ethene and cis-Butadiene==

cis-Butadiene and ethene were modeled in GaussView 03, and optimised in Gaussian. The semi-empirical AM1 method was utilised and the molecular orbitals were visualised and are illustrated below:

Relative energy, and symmetry in relation to the σv plane are also indicated.

<center>

{| border="1"
!Molecule
!Total Energy of Molecule (a.u)
!HOMO energy (a.u)
!Visualised HOMO
!HOMO Symmetry (with respect to σv plane)
!LUMO Energy (a.u)
!Visualised LUMO
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.026
| -0.39
|[[Image:ajm308EtheneHOMO.jpg|thumb|]]
|Symmetric
|0.052
|[[Image:ajm308EtheneLUMO.jpg|thumb|]]
|Antisymmetric
|----
|Cis-butadiene
|0.049
| -0.34
|[[Image:ajm308CBHOMO.jpg|thumb|]]
|Antisymmetric
|0.017
|[[Image:ajm308CBLUMO.jpg|thumb|]]
|Symmetric
|----
|}

</center>

Only orbitals of identical symmetry have the required overlap density for the reaction to proceed, and so it can be seen that the HOMO of cis-butadiene can interact with the LUMO of ethene, and vice versa.

===Transition States===

The overlap between the two sets of pi orbitals is maximised by adopting an envelope type structure. In order to obtain the starting geometry a bicyclic system was modeled, and the -CH2-CH2- fragment removed. Inter-fragment distance was then guessed to be 2.15 A.

Optimisation was then carried out, using methodology similar to that found in Section xxx above.

One imaginary frequency was found to be -818 cm-1. This vibration is visualised below and shows synchronous bond forming, concurring with the concerted nature of pericyclic reactions.

<center>

[[Image:DAvibsajm308.gif]]

</center>

The lowest real vibrational frequency is observed at 167 cm-1 and is attributed to the rocking of the CH2=CH2 section of the transition structure.

The energy of the transition structure was found to be -231.60 a.u.

The HOMO and LUMO of the transition state were also visualised and are shown below:

<center>

[[Image:HOMODAajm308.jpg|thumb|center|]]

[[Image:LUMODAajm308.jpg|thumb|center|]]

</center>

The HOMO is antisymmetric, and can be associated with overlap of the HOMO of cis-butadiene and the LUMO of ethene - where two antisymmetric molecular orbitals overlap.

Similarly, the LUMO is symmetric, and can be associated with overlap of the LUMO of cis-butadiene and the HOMO of ethene.

The geometry of the transition structure is outlined in the table below.

<center>

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C Length
| -
|2.21 A
|----
|Ethene C=C Length
|1.33 A
|1.38 A
|----
|Butadiene C=C Length
|1.34 A
|1.37 A
|----
|Butadiene C-C Length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C Angle
|125.6°
|121.5°
|----
|}

</center>

The C-C, that is only partially formed in the transition state, is markedly longer than any other bond present as a result of this. C-C and C=C bonds are no longer differentiable in the transition state, as they are in the reactants. Typical sp3 C-C bond lengths of 1.54 A <ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref> correlate well with the calculated C-C bond distance in butadiene. Calculated sp2 C=C bond lengths of 1.34 A and 1.33 A correlate very well with the typical values.

The Van der Waal's radius of the C atom is 1.7 A. <ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

==Cyclohexa-1,3-diene with Maleic Anhydride==

The reaction of cyclohexa-1,3-diene and maleic anhydride yields the endo product in majority. The reaction proceeds under kinetic control so it assumed that the exo transition state is at higher energy.

[[Image:Ajm308reactionscheme.gif|center|]]

===Transition States===

Again, bicyclic systems were used in order to model the transition states for both the endo and exo products. 2.2 A was used as an initial guess for the inter-fragment distances, and both structures were optimised using the 'Optimisation to TS (Berny)' method, as outlined in section xxx above.

Frequency analysis was also performed.

Geometric and thermochemical properties, as well as the imaginary vibrational motions returned are displayed in the table below:

<center>

{| border="1"
|Property
|Exo
|Endo
|----
|Product Energy (a.u)
| -0.16
| -0.16
|----
|Transition State Energy (a.u)
|-0.051
|-0.052
|----
|Imaginary Vibrational Frequency (cm-1)
| -812
| -806
|----
|Imaginary Vibration Animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest Real Frequency (cm-1)
|61
|62
|----
|Lowest Real Frequency Assignment
|Rocking of Cyclohexadiene Fragment
|Rocking of Cyclohexadiene Fragment
|----
|Fragment Bond Distance (A)
|2.17
|2.16
|----
|(C=O)-C-(C=O) Through Space Distance (A)
|2.28
|2.28
|----
|C=C Distance (A)
|1.40
|1.40
|----
|C-C Bridge Distance (A)
|1.52
|1.52
|----
|HOMO
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

</center>

The thermochemical properties are in agreement with the prediction that the endo product will be major, the exo minor. The endo transition state has a lower transition state than the exo transition state, and as the reaction is under kinetic control, is favoured as the reaction energy barrier is smaller.

The HOMOs visualised above show differences between the endo and exo transition states, in the -(C=O)-O-(C=O)- region. The endo transition state has appreciable electron density in the region, however, the exo transition state does not. There is clearly more secondary orbital effects operating in the endo transition state, than in the exo transition state. The transition state is stabilised by these interactions, thus lowering the energy of the endo transition state relative to the exo transition state. This secondary orbital interaction is shown in the diagram below:

!!!Diagram!!!

=Conclusions=

Once again, the power of computational chemistry is apparent, as is the need to balance the desired accuracy of the calculations against computational cost and time constraints. One example is when using the QST2 method which is more efficient than the QST3 method, but has the potential to fail if reactants and products are not close to the transition structure. It seems it is often worth utilising a lower level protocol initially, and if the desired results are not obtained, then a higher level calculation should be carried out.

The wide range of information gleaned from the computational methods, and close correlation with experimental results, means computational chemistry rightly deserves a place alongside more traditional methods of experimentation.

Limitations of the field are also apparent in accounting for more complex physical phenomena, such as solvent effects.

=References=

<references/>