ChemWiki - User contributions [en]

Rep:Mod:3992

2011-12-16T15:29:28Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|thumb|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|thumb|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|thumb|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|100px]] || [[Image:ButadieneHOMObem.png|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|thumb|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|100px]] || [[Image:TSHOMObem.png|100px]] || [[Image:TSHOMO-1bem.png|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|100px]] || [[Image:EndoTSFreq1.png|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the HOMO and LUMO there is little secondary orbital effect, but this does not rule out the possibility that there is a large stabilisation in any other orbitals, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T15:29:00Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|thumb|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|thumb|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|thumb|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|100px]] || [[Image:ButadieneHOMObem.png|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|thumb|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|100px]] || [[Image:TSHOMObem.png|100px]] || [[Image:TSHOMO-1bem.png|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|100px]] || [[Image:EndoTSFreq1.png|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the HOMO and LUMO there is little secondary orbital effect, but this does not rule out the possibility that there is a large stabilisation in any other orbitals, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T15:28:14Z

Bem09: /* The Basic Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|thumb|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|thumb|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|thumb|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|100px]] || [[Image:ButadieneHOMObem.png|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|thumb|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|100px]] || [[Image:TSHOMObem.png|100px]] || [[Image:TSHOMO-1bem.png|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the HOMO and LUMO there is little secondary orbital effect, but this does not rule out the possibility that there is a large stabilisation in any other orbitals, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T15:27:30Z

Bem09: /* Cope Rearrangement Tutorial */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|thumb|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|thumb|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|thumb|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the HOMO and LUMO there is little secondary orbital effect, but this does not rule out the possibility that there is a large stabilisation in any other orbitals, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:2992

2011-12-16T15:26:49Z

Bem09: /* Molecular Orbital Analysis of BH3 */

= Module 2: Bonding (Ab initio and density functional molecular orbital. ''Bethan Matthews'' =
== Optimisation, Vibrational Analysis and Molecular Orbital Analysis of BH3 and TlBr3 ==
=== Optimisation of BH3 ===

The molecule of BH3 was built in Gaussview and optimised (<jmolFile text="Jmol">BH3Optimisation.mol</jmolFile>), giving the following summary ([http://hdl.handle.net/10042/to-10636 D-SPACE]):

{| class="wikitable" border="1"
|+ Table 1: Summary of details from optimisation of BH3.
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Final Energy || -26.4623 a.u.
|-
| Gradient || 0.0002 a.u.
|-
| Dipole Moment || 0.000 Debye
|-
| Point Group || D3h
|-
| Time Taken || 26 seconds
|}

It was checked to see if it had run to completion, by looking at whether it had converged (log file).

The following graphs in figure 1 show the energy and gradients for each step of the optimisation. The process terminates when the gradient is minimised (or approximately zeroed).

[[Image:BH3Graphs.png|thumb|500px|centre|'''Figure 1: Graphs showing optimisation steps of BH3.''' ]]

The energy at each step is calculated, with the aim of obtaining a minimum. The process runs until the energy decrease each time is negligible. This is shown in the gradient vs. step graph, where the final step has a gradient of approximately 0.0002 a.u. which is acceptable.

The optimised molecule of BH3 gives a computed B-H bond length of 1.19Å. This is in agreement of literature<ref>Jonas, V., Frenking, G. and Reetz. M.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 8741</ref>. The optimal H-B-H bond angle is 120°, which fits with what is known about the structure of BH3 as trigonal planar. The advantage of using a computational analysis for the study of this molecule is the fact we can carry out theoretical calculations on a molecule which only exists as a monomer in the gas phase.

=== Vibrational Analysis of BH3 ===

Performing frequency analysis can help identify whether or not we have a global minimum or not. If there are no negative frequencies calculated then the ground state configuration has been found.
The vibrational analysis of the above optimised molecule ([http://hdl.handle.net/10042/to-10638 D-SPACE]) gives an interesting infra red spectrum, as shown below.

[[Image:BH3IR.png|thumb|500px|centre|'''Figure 2: IR spectrum of the optimised BH3 molecule.''' ]]

The following table summarises the seperate bend and stretch modes which are obtained.

{| class="wikitable" border="1"
|+ Table 2: Summary of IR stretching and bending modes for BH3.
! Mode !! Frequency (cm-1) !! Intensity !! Description of mode !! Symmetry label, for D3h point group
|-
| '''1''' [[Image:BH3Freq1.png|thumb|100px]] || 1144.15 || 92.87 || H-atoms all move up and down, above and below the plane of the B-atom simultaneously, the B-atom moving in the opposite direction. (Umbrella bend) || A2"
|-
| '''2''' [[Image:BH3Freq2.png|thumb|100px]] || 1203.64 || 12.31 || B-H unit remains still, the other two H-atoms bend towards each other and back again simultaneously. (Scissor) || E'
|-
| '''3''' [[Image:BH3Freq3.png|thumb|100px]] || 1203.64 || 12.32 ||B-atom stays still and H-atoms all bend simultaneously. (Rock)|| E'
|-
| '''4''' [[Image:BH3Freq4.png|thumb|100px]] || 2598.42 || 0.00 || B-atom stays still and H-atoms stretch away from B-atom and back simultaneously. (Symmetric Stretch) || A1'
|-
| '''5''' [[Image:BH3Freq5.png|thumb|100px]] || 2737.44 || 103.74 || B-H unit remains still, other two H-atoms stretch away from B-atom in a concerted manner. (Asymmetric Stretch) || E'
|-
| '''6''' [[Image:BH3Freq6.png|thumb|100px]] || 2737.44 || 103.73 || B-atom stays still, two H-atoms stretch out and back simultaneously, the remaining H-atom stretches out and back opposite to the other two H-atoms. (Asymmetric Stretch) || E'
|}

The IR shows three peaks at 1144.15, 1203.64 and 2737.44cm-1, although the vibrational analysis suggests there are six vibrational modes. It can be seen from the table that some of the modes have the same frequency and intensity, so on the spectrum they would not be distinguishable, (2 and 3, and 5 and 6). This is one benefit of the vibrational analysis. In addition to this, the peak at 2598.42cm-1 has an intensity of zero so it does not show up on the spectrum. This is because the stretch is totally symmetrical, and it cannot be detected as there is no change in dipole moment.

=== Molecular Orbital Analysis of BH3 ===

The molecular orbitals (MO) for BH3 were calculated using B3LYP/6-31G basis set ([http://hdl.handle.net/10042/to-10505 D-SPACE]).

{| class="wikitable" border="1"
|+ '''Table 3: Summary of the molecular orbitals of BH3 as calculated using B3LYP/6-31G basis set.'''
| '''Energy''' || 0.192 || 0.189 || 0.189 || -0.075 || -0.357 || -0.357 || -0.518 || -6.730
|-
| '''Shape''' || [[Image:BH3MO8.png|thumb|75px]] || [[Image:BH3MO7.png|thumb|75px]] || [[Image:BH3MO6.png|thumb|75px]] || [[Image:BH3MO5.png|thumb|75px]] || [[Image:BH3MO4.png|thumb|75px]] || [[Image:BH3MO3.png|thumb|75px]] || [[Image:BH3MO2.png|thumb|75px]] || [[Image:BH3MO1.png|thumb|75px]]
|-
| '''Notes''' || || colspan="2" | Degenerate || LUMO || || colspan="2" | Degenerate, HOMO ||
|}

If we compare the calculated molecular orbitals to the liner combination of atomic orbitals (LCAO), the following MO diagram is obtained. The 1s boron orbital is generally considered too low in energy to participate in bonding, and so is ignored for the purpose of this diagram.

[[Image:BH3MODiagram.png|thumb|centre|500px|'''Figure 4: MO diagram of BH3, with comparison of calculated MO with LCAO.''']]

There are no significant differences between the different methods, both giving identifiably similar orbital shapes. This leads to the conclusion that for this molecule, each approach is valid. The LCAO approach is merely qualitative, but the computed MOs have an energy assigned. This is much more useful when trying to consider the ordering of the orbitals and their relative stabilities.

=== NBO Analysis of BH3 ===
[[Image:BH3NBO.png|thumb|150px|Figure 3: NBO analysis of BH3, giving the charge distribution.]]
The NBO analysis of BH3 gives a charge distribution as shown in Figure 3. The value of the boron atom is 0.332eV, and the hydrogens each have a value of -0.111eV. This is reasonable, as the boron is highly electron deficient, only having six valence electrons in this molecule. This electron deficiency is why it acts as such a good Lewis acid, and also why it prefers to dimerise to B2H6. These charges cancel out over all, leaving the molecule neutral.

From the .log files, we can look at the type of bonds that are formed. We expect an sp2 hybridisation, so the bonding orbitals on the boron atom are expected to be approximately 33% s-character and 66% p-character. The hydrogen atoms are expected to bond through s-orbitals.

{| class="wikitable" border="1"
|+ '''Table 4: Summary of bond characteristics for BH3.'''
! Atom !! Contribution to bond (%) !! s-Character (%) !! p-Character (%)
|-
| B || 44.48 || 33.33 || 66.66
|-
| H || 55.52 || 100.00 || 0.00
|-
| LP || Not included || 100.00 || 0.00
|}

=== Optimisation of TlBr3 ===

The molecule of TlBr3 was built in Gaussview and optimised ([http://hdl.handle.net/10042/to-10639 D-SPACE]) to give a summary as shown below in table 4. (<jmolFile text="Jmol">TlBr3OptimisationBEM.mol</jmolFile>). As it is a relatively large molecule, with a total of 151 electrons, we have to use a pseudopotential. This models the core orbitals of the atoms, as they are not majorly involved in the bonding.

{| class="wikitable" border="1"
|+ '''Table 5: Summary of optimisation of TlBr3.'''
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Final Energy || -91.2181 a.u.
|-
| Gradient || 0.0000 a.u.
|-
| Dipole Moment || 0.000 Debye
|-
| Point Group || D3h
|-
| Time Taken || 24 seconds
|}

This optimisation gave a Tl-Br bond length of 2.65Å, and a bond angle of 120°.

=== Vibrational Analysis of TlBr3 ===

The vibrational analysis of the above optimised molecule gives an interesting infra red spectrum, as shown below.

[[Image:TlBr3IR.png|thumb|500px|centre|'''Figure 5: IR spectrum of the optimised TlBr3 molecule.''' ]]

The following table summarises the seperate bend and stretch modes which are obtained.

{| class="wikitable" border="1"
|+ Table 6: Summary of IR stretching and bending modes for TlBr3.
! Mode !! Frequency (cm-1) !! Intensity !! Description of mode !! Symmetry label, for D3h point group
|-
| '''1''' [[Image:TlBr3Freq1.png|thumb|100px]] || 46.43 || 3.69 || Tl-Br unit stays still, the other two Br atoms bend towards each other and back in a concerted motion. (Scissor) || E'
|-
| '''2''' [[Image:TlBr3Freq2.png|thumb|100px]] || 46.43 || 3.69 || Tl-atom stays still and Br-atoms all bend simultaneously. (Rock) || E'
|-
| '''3''' [[Image:TlBr3Freq3.png|thumb|100px]] || 52.14 || 5.85 || Br-atoms all move up and down, above and below the plane of the B-atom simultaneously, the Tl-atom moving in the opposite direction. (Umbrella) || A2"
|-
| '''4''' [[Image:TlBr3Freq4.png|thumb|100px]] || 165.27 || 0.00 || Tl-atom stays still and Br-atoms stretch away from B-atom and back simultaneously. (Symmetric Stretch) || A1'
|-
| '''5''' [[Image:TlBr3Freq5.png|thumb|100px]] || 210.69 || 25.48 || Tl-Br unit remains still, other two Br-atoms stretch away from Tl-atom in a concerted manner. (Asymmetric Stretch) || E'
|-
| '''6''' [[Image:TlBr3Freq6.png|thumb|100px]] || 210.69 || 25.48 || Tl-atom stays still, two Br-atoms stretch out and back simultaneously, the remaining Br-atom stretches out and back opposite to the other two Br-atoms. (Asymmetric Stretch) || E'
|}

Again we can see degeneracy of the vibrations, modes 1 and 2, and 5 and 6. This shows up as one peak on the IR spectrum. Again the lack of a change in dipole in the fully symmetric stretch at mode 4 results in a zero intensity peak and therefore a lack of its presence on the IR spectrum. There are no negative frequencies shown, which suggests we have found the ground state configuration. If we look at the low frequencies in the .log file, we can see that although there are some negative frequencies, they are all more positive than -10cm-1 and can therefore be neglected.

Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449

== ''Cis''- and ''Trans''- Isomers of [Mo(CO)4(PCl3)2] ==

Note that Gaussview removes some bonds, where it cannot interpret the lengths correctly, thinking they are too long to be actual bonds. This short coming has been ignored, and it primarily occurs in the P-Cl bonds and occasionally in the Mo-P bonds. This is because Gaussview has a list of mainly organic bond lengths, and the bonds created in this molecule do not fit within these parameters. As chemists we represent a bond as a line, and this line can be as long or as short as we draw it. However, Gaussview does not understand this, and has to assign bonds based on the separation distance between two atoms. This is vaguely unhelpful, as for inorganic compounds the bonds do not always follow this ideal distance, especially in transition metals. Technically the bond shouldn't be based too much on the separation distance, as there are other factors which come into play when determining the length of the bond, (electrons being present to form the bond, the ratio of the number of atoms to the number of electrons available to form the bonds etc.) This problem also manifests itself in the sulphuric acid mini project, where you would conventionally draw the molecule with 2 S=O and one S-O-. This causes a problem with the bond lengths, as they are actually resonance forms, with a bond length sort of in between a single S-O and a double S-O.

=== Optimisation of ''Trans''-[Mo(CO)4(PCl3)2] ===

The molecule was primarily optimised using a loose convergence limit and a relaxed basis set, in order to obtain an optimised molecule which could then be further be optimised, after a few manual manipulations to the molecule, which computational methods fails to perform. Note that Gaussview removes some bonds, where it cannot interpret the lengths correctly, thinking they are too long to be actual bonds. This short coming has been ignored, and it primarily occurs in the P-Cl bonds and occasionally in the Mo-P bonds.

{| class="wikitable" border="1"
|+ '''Table 7: Optimisation of ''Trans''-[Mo(CO)4(PCl3)2]'''
! !! Optimisation 1 !! Optimisation 2
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RB3LYP || RB3LYP
|-
| Basis Set || LANLZ2MB || LANL2DZ
|-
| Charge || 0 || 0
|-
| Spin || singlet || singlet
|-
| E(RB3LYP) || -617.522 a.u. || -623.576 a.u.
|-
| RMS Gradient Norm || 0.0000 a.u. || 0.0000 a.u.
|-
| Dipole Moment || 0.0000 Debye || 0.3053 Debye
|-
| Point Group || C1 || C1
|-
| Time Taken || 7 minutes, 29.8 seconds || 40 minutes, 27.4 seconds
|-
| D-Space || [http://hdl.handle.net/10042/to-10731 Optimisation 1] || [http://hdl.handle.net/10042/to-10741 Optimisation 2]
|-
| Jmol || <jmolFile text="Optimisation 1">TransMoCO4PCl32.mol</jmolFile> || <jmolFile text="Optimisation 2">TransMoCO4PCl32Opt2.mol</jmolFile>
|}

From this optimised structure, we can look at the bond angles and bond lengths.

{| class="wikitable" border="1"
|+ '''Table 8: Optimised bond angles and bond lengths.'''
! Bond !! Computed Bond Length /Å !! Bond !! Computed Bond Angle /°
|-
| Mo-P || 2.44 || rowspan="2" | P-Mo-C || rowspan="2" | 90
|-
| P-Cl || 2.24
|-
| Mo-C || 2.06 || rowspan="2" | C-Mo-C || rowspan="2" | 179, 90
|-
| C=O || 1.17
|}

These bond angles are as expected for an octahedral geometry. The angles are only quoted to the nearest whole number due to accuracy problems, which explains the angle of 179° rather than the ideal of 180°. This can mainly be attributed to the computational weaknesses, and maybe increasing the accuracy of the basis set and pseudopotentials will allow for more idealised values.

=== Vibrational Analysis of ''Trans''-[Mo(CO)4(PCl3)2] ===

One way to identify which isomer you have is to use IR spectroscopy, but this is only useful if the two isomers have distinctly different spectra. The frequency analysis was run using the same basis set and method as the second optimisation, important as we don't want to induce any other changes. By comparison of the details from the summary below and the one above, we can confirm that we are indeed running frequency analysis on the fully optimised molecule rather than the partially optimised molecule.

{| class="wikitable" border="1"
|+ '''Table 9: Summary of frequency analysis of ''Trans''-[Mo(CO)4(PCl3)2]
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || singlet
|-
| E(RB3LYP) || -623.576 a.u.
|-
| RMS Gradient Norm || 0.0000 a.u.
|-
| Imaginary Frequency || 0
|-
| Dipole Moment || 0.3053 Debye
|-
| Point Group || C1
|-
| Time Taken || 30 minutes, 24.4 seconds
|-
| D-SPACE || [http://hdl.handle.net/10042/to-10773 Frequency Analysis]
|}

The IR spectrum is shown below.

[[Image:TransMoCO4PCl32IR.png|thumb|500px|centre|'''Figure 6: IR spectrum of the optimised ''Trans''-[Mo(CO)4(PCl3)2.]]

The carbonyl stretches are not degenerate in this molecule, although we expect them to be, due to the high symmetry of the molecule. The table below summarises the relevant stretches. Only one peak is expected, due to the fact all carbonyls are axial and therefore the same.

{| class="wikitable" border="1"
|+ '''Table 10: Summary of carbonyl stretches in the vibrational frequencies of ''Trans''-[Mo(CO)4(PCl3)2].'''
! Mode !! Frequency /cm-1 !! Intensity !! Description of Mode
|-
| [[Image:TransMoCO4PCl32Freq42.PNG|thumb|100px|centre|'''42''']] || 1950.52 || 1475.41 || Asymmetric stretching of one pair of trans carbonyls.
|-
| [[Image:TransMoCO4PCl32Freq43.PNG|thumb|100px|centre|'''43''']] || 1951.16 || 1466.73 || Asymmetric stretching of the other pair of trans carbonyls.
|-
| [[Image:TransMoCO4PCl32Freq44.PNG|thumb|100px|centre|'''44''']] || 1977.43 || 0.64 || Symmetric stretching of a pair of trans carbonyls, in a concerted mechanism with the other pair.
|-
| [[Image:TransMoCO4PCl32Freq45.PNG|thumb|100px|centre|'''45''']] || 2031.21 || 3.77 || Symmetric stretching of all four carbonyl ligands.
|}

=== Optimisation of ''Cis''-[Mo(CO)4(PCl3)2] ===

{| class="wikitable" border="1"
|+ '''Table 11: Optimisation of ''Cis''-[Mo(CO)4(PCl3)2]'''
! !! Optimisation 1 !! Optimisation 2
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RB3LYP || RB3LYP
|-
| Basis Set || LANLZ2MB || LANL2DZ
|-
| Charge || 0 || 0
|-
| Spin || singlet || singlet
|-
| E(RB3LYP) || -617.525 a.u. || -623.577 a.u.
|-
| RMS Gradient Norm || 0.0003 a.u. || 0.0000 a.u.
|-
| Dipole Moment || 8.4926 Debye || 1.3093 Debye
|-
| Point Group || C1 || C1
|-
| Time Taken || 10 minutes, 11.3 seconds || 1 hour, 4 minutes, 40.9 seconds
|-
| D-Space || [http://hdl.handle.net/10042/to-10732 Optimisation 1] || [http://hdl.handle.net/10042/to-10774 Optimisation 2]
|-
| Jmol || <jmolFile text="Optimisation 1">CisMoCO4PCl32.mol</jmolFile> || <jmolFile text="Optimisation 2">CisMoCO4PCl32Opt2.mol</jmolFile>
|}

From this optimised structure, we can look at the bond angles and bond lengths.

{| class="wikitable" border="1"
|+ '''Table 12: Optimised bond angles and bond lengths.'''
! Bond !! Computed Bond Length /Å !! Bond !! Computed Bond Angle /°
|-
| Mo-P || 2.51 || rowspan="2" | P-Mo-C || rowspan="2" | 176, 89
|-
| P-Cl || 2.34
|-
| Mo-C || eq=2.06, ax=2.01 || rowspan="2" | C-Mo-C || rowspan="2" | 178, 90, 87 between two equatorial
|-
| C=O || 1.17
|}

These angles are approximately what are expected from an octahedral molecule. The two PCl3 ligands cause a slight compression of the two equatorial carbonyl ligands, which is reflected in the angle of 87°, which is slightly lower than the ideal ligand of 90°.

=== Vibrational Analysis of ''Cis''-[Mo(CO)4(PCl3)2] ===

{| class="wikitable" border="1"
|+ '''Table 13: Summary of frequency analysis of ''Cis''-[Mo(CO)4(PCl3)2]
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || singlet
|-
| E(RB3LYP) || -623.577 a.u.
|-
| RMS Gradient Norm || 0.0000 a.u.
|-
| Imaginary Frequency || 0
|-
| Dipole Moment || 1.3090 Debye
|-
| Point Group || C1
|-
| Time Taken || 31 mintues, 5.8 seconds
|-
| D-SPACE || [http://hdl.handle.net/10042/to-10776 Frequency Analysis]
|}

The IR spectrum is shown below.

[[Image:CisMoCO4PCl32IR.PNG|thumb|500px|centre|'''Figure 7: IR spectrum of the optimised ''Cis''-[Mo(CO)4(PCl3)2.]]

The table below summarises the relevant stretches. We expect two types of peak, one for the axial carbonyl and one for the equatorial carbonyl.

{| class="wikitable" border="1"
|+ '''Table 14: Summary of carbonyl stretches in the vibrational frequencies of ''Cis''-[Mo(CO)4(PCl3)2].'''
! Mode !! Frequency /cm-1 !! Intensity !! Description of Mode
|-
| [[Image:CisMoCO4PCl32Freq42.PNG|thumb|100px|centre|42]] || 1945.15 || 760.20 || Asymmetric stretching of the two equatorial carbonyls.
|-
| [[Image:CisMoCO4PCl32Freq43.PNG|thumb|100px|centre|43]] || 1948.88 || 1500.64 || Asymmetric stretching of the two axial carbonyls.
|-
| [[Image:CisMoCO4PCl32Freq44.PNG|thumb|100px|centre|44]] || 1958.32 || 636.42 || Symmetric stretching of the two equatorial carbonyls, with axial carbonyls stretching symmetrically in a concerted mechanisms.
|-
| [[Image:CisMoCO4PCl32Freq45.PNG|thumb|100px|centre|45]] || 2023.42 || 594.64 || Symmetric stretching of all carbonyls.
|}

=== Comparison of ''Cis''-[Mo(CO)4(PCl3)2] and ''Trans''-[Mo(CO)4(PCl3)2] ===

From the above results, you can see that the ''cis'' isomer is slightly more stable than the ''trans'' isomer. The energy difference is sufficiently small enough (2.63kJ mol-1) that the isomerisation can take place at room temperature. This is agreeable with the process described in literature.<ref>Hogarth, G., Norman, T.; ''Inorg. Chim. Acta''; '''1997'''; ''254''; 167</ref>

In the ''trans'' form, the PCl3 groups are far apart, and there is little steric hinderence. In comparison, the ''cis'' form has the PCl3 groups next to each other, which causes a destabilisation. However, this is not in agreement with the data calculated above, so there must be another angle to look at. If you consider the magnitudes of the trans effect of each group, this can help explain it. The trans effect of the carbonyls is slightly smaller than the PCl3 groups, and therefore stabilise the trans group when they are placed opposite each other. If the PCl3 groups are opposite each other, this causes a relative destabilisation. You can alter the order of stability of ''cis'' and ''trans'' isomers by changing the PCl3 ligand for a ligand with a smaller trans effect.

== Sulphuric Acid ==

[[Image:Scheme.PNG|thumb|500px|centre|'''Figure 8: Reaction equilibrium for the protonation of sulphuric acid.''']]

The molecules were first optimised using a low accuracy basis set to give the follow summary.
{| class="wikitable" border="1"
|+ '''Table 15: Summary of optimisation of sulphuric acid equilibrium.'''
! Quality !! H2 !! S2O62- !! S2O6H2
|-
| Calculation Type || FOPT || FOPT || FOPT
|-
| Calculation Method || RB3LYP || RB3LYP || RB3LYP
|-
| Basis Set || 3-21G || 3-21G || 3-21G
|-
| Charge || 0 || 2- || 0
|-
| Spin || singlet || singlet || singlet
|-
| E(RB3LYP) || -1.17 a.u. || -1240.90 a.u. || -1242.09 a.u.
|-
| RMS Gradient Norm || 0.000 a.u. || 0.000 a.u. || 0.000 a.u.
|-
| Dipole Moment || 0.0000 Debye || 0.0000 Debye || 0.0071 Debye
|-
| Point Group || D*h || C1 || C1
|-
| Time Taken || 12s || 1m54.5s || 2m57.9s
|-
| D-SPACE || [http://hdl.handle.net/10042/to-10864 Optimisation 1] || [http://hdl.handle.net/10042/to-10865 Optimisation 1] || [http://hdl.handle.net/10042/to-10866 Optimisation 1]
|-
| Jmol || <jmolFile text="Optimisation 1">H2Opt1.mol</jmolFile> || <jmolFile text="Optimisation 1">S2O62-Opt1.mol</jmolFile> || <jmolFile text="Optimisation 1">S2O6H2Opt1.mol</jmolFile>
|}

Obviously, these energies are clearly quite high, so for the next optimisation, which was done with a more accurate basis set etc, the molecule was rearrange slightly, as seen in the next Jmols.

{| class="wikitable" border="1"
|+ '''Table 16: Summary of optimisation of sulphuric acid equilibrium.'''
! Quality !! H2 !! S2O62- !! S2O6H2
|-
| Calculation Type || FOPT || FOPT || FOPT
|-
| Calculation Method || RB3LYP || RB3LYP || RB3LYP
|-
| Basis Set || LANL2DZ || LANL2DZ || LANL2DZ
|-
| Charge || 0 || 2- || 0
|-
| Spin || singlet || singlet || singlet
|-
| E(RB3LYP) || -1.17 a.u. || -471.17 a.u. || -472.28 a.u.
|-
| RMS Gradient Norm || 0.000 a.u. || 0.000 a.u. || 0.000 a.u.
|-
| Dipole Moment || 0.0000 Debye || 0.0003 Debye || 3.6255 Debye
|-
| Point Group || D*h || C1 || C1
|-
| Time Taken || 11.3s || 1m57.1s || 9m24.8s
|-
| D-SPACE || [http://hdl.handle.net/10042/to-10873 Optimisation 2] || [http://hdl.handle.net/10042/to-10876 Optimisation 2] || [http://hdl.handle.net/10042/to-10881 Optimisation 2]
|-
| Jmol || <jmolFile text="Optimisation 2">H2Opt2.mol</jmolFile> || <jmolFile text="Optimisation 2">S2O62-Opt3.mol</jmolFile> || <jmolFile text="Optimisation 2">S2O6H2Opt3.mol</jmolFile>
|}

From these optimisations, the bonds disappeared, which is just Gaussview telling us the bonds are not perfectly matched to his list of ideal organic bonds. However, in S2O62- there are a number of equivalent resonance structures, which results in these bonds all appearing equivalent (1.616Å). In S2O6H2 there is a difference in the bond lengths between the S=O(1.59Å) and the S-O (1.77Å). These are both as expected, which is quite a useful computation, as occasionally the methods do not use any sort of chemistry and just take the structure as drawn.

In terms of the energy change of the equilibrium shown above:
The left hand side has a total energy of 101.62kJ mol-1, the right hand side has a total energy of 123.14kJ mol-1. This gives an energy change of forward - backwards = 21.52kJ mol-1. These values were taken from the thermochemistry sections of the log files for the frequency calculations. ([http://hdl.handle.net/10042/to-10916 H2] [http://hdl.handle.net/10042/to-10900 S2O62-] [http://hdl.handle.net/10042/to-10902 S2O6H2] This calculation shows that the molecule prefers the dissociated state, although the energy change is relatively low, so the reaction is probably in equilibrium at room temperature (or at least only just above).

If we obtain the LUMO values for S2O62- and S2O6H2, we can see that the S2O6H2 has a LUMO which is lower in energy.
{| class="wikitable" border="1"
|+
| [[Image:S2O62-LUMO.png|thumb|100px|S2O62-]] || [[Image:S2O6H2LUMO.png|thumb|100px|S2O6H2]]
|-
| 0.13 || -0.25
|}

This is because the effect the negative charge has on the energy levels is to raise them slightly. We can also look at the structures of the MOs. If we first examine the S2O62- LUMO: The main S-S bond is strongly antibonding in character, this is likely to cause a large destabilisation, contributing to the higher energy of the MO. In contrast, the oxygens all bond to the sulphur in a normal bonding way, this allows some weaker through-space bonding-type interactions between all the oxygens, which causes a slight stabilisation effect. There are 5 obvious nodes in this moleculur orbital. If we compare this to the S2O6H2 LUMO, there is a similar anti-bonding in character S-S bond. Again, the oxygens all have the same bonding orientation, allowing through-space bonding-type interactions, as above. There is also the fully bonding interaction between the H and the O, again, a favourable interaction. This MO is more negative in energy, as it is not an anion.

[[Image:S2O6H2MO13.png|thumb|100px|'''Figure 9: S2O6H2 MO 13.]]
If we consider the other MOs for S2O6H2, the six which are lowest in energy are all centred on the oxygen atoms, which is to be expected, as the higher electronegativity of the oxygen atoms than the sulphur atoms causes the MOs to be lower in energy. MO 7 is the completely bonding orbital which is relatively boring and also expected. If we jump to MO 13, this MO is quite intersting. The S-S bond is total bonding in character, but all the S-O interactions are anti-bonding in character. This is clearly quite a large destabilisation effect, but if you consider the weaker through-space interactions, there are number of bonding character interactions, which help to counteract the destabilisation effect. There is also the O-H bond, which in this MO is bonding in character. In fact, the O-H bond is bonding in character (or not part of the MO) all the way through the lower energy bonding orbitals, it's not until the really high energy MOs are examined that we find the O-H bond being anti-bonding in character.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T15:24:21Z

Bem09: /* Optimizing the "Chair" and "Boat" Transition Structures */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the HOMO and LUMO there is little secondary orbital effect, but this does not rule out the possibility that there is a large stabilisation in any other orbitals, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T12:28:07Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

Rep:Mod:3992

2011-12-16T12:26:43Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products. <ref>Craig, D., Shipman, J.J. and Fowler, R.B.; </ref>
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T12:26:26Z

Bem09: /* References */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==
<references/>

Rep:Mod:3992

2011-12-16T12:26:03Z

Bem09: /* Cope Rearrangement Tutorial */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation. <ref>Hoffmann R. and Stohrer, W.D.; ''J. Am. Chem. Soc.''; '''1971'''; ''93''; 6941</ref>

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K <ref>Wiest, O., Black, K.A. and Houk K.N.; ''J. Am. Chem. Soc.''; '''1994'''; ''116''; 10336</ref>
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==

Rep:Mod:3992

2011-12-16T12:25:35Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== References ==

Rep:Mod:3992

2011-12-16T12:25:09Z

Bem09:

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair- or boat-like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ==

Rep:Mod:3992

2011-12-15T21:20:30Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': [http://hdl.handle.net/10042/to-11392 D-SPACE]
''Exo'': [http://hdl.handle.net/10042/to-11395 D-SPACE]
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

Rep:Mod:3992

2011-12-15T17:58:46Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å. This smaller destabilisation results in the ''endo'' form having a lower energy transition state.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed. As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product. Also looking at the structures produced, there seems a suitable progression to a suitable product, so the transition state found above seems vaguely correct.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product, as well as the kinetic product.

File:EndoVDWbem.png

2011-12-15T16:01:24Z

Bem09:

File:ExoVDWbem.png

2011-12-15T16:01:05Z

Bem09:

Rep:Mod:3992

2011-12-15T16:00:47Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''exo'' VdW repulsions.]] || [[Image:EndoVDWbem.png|thumb|100px| Possible ''endo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed.
For ''exo'':
[[Image:ExoIRC.JPG‎|centre|500px|Figure 8: IRC for the ''exo'' form.]]
For ''endo'':
[[Image:EndoIRC.JPG‎|centre|500px|Figure 9: IRC for the ''endo'' form.]]
As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

Rep:Mod:3992

2011-12-15T15:59:53Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844,anti-symmetric]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214,anti-symmetric]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773,anti-symmetric]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228,anti-symmetric]]
|}

In the ''endo'' form you can sort of see that a possible secondary orbital interaction may occur, although in this reaction it is small if it occurs at all, so the cause for the ''endo'' preference may be due to steric effects. If we look at the structures of the transition states, the ''endo'' form has partially formed bonds which are 2.27Å in length, and in the ''exo'' form they are 2.29Å. There is slight Van der Waals repulsion between the maleic C=O carbon and the hydrogen as shown below, as the sum of their VdW radii is 2.90Å, larger than the separation distance. This does not occur in the ''endo'' form, as the pair is not as close (opposite ends of the molecule!) and the other hydrogens are not close enough to cause an effect. However, there is a much smaller, but still repulsive, VdW between the hydrogens as shown below, as the sum of their VdW radii is 2.40Å.

{| class="wikitable" border="1"
| [[Image:ExoVDWbem.png|thumb|100px|Possible ''endo'' VdW repulsions.]] || [[Image:ExoVDWbem.png|thumb|100px| Possible ''exo'' VdW repulsions.]]
|}

To check that these transition states lead to suitable products we can run an IRC and see that a minimum is formed.
For ''exo'':
[[Image:ExoIRC.JPG‎|centre|500px|Figure 8: IRC for the ''exo'' form.]]
For ''endo'':
[[Image:EndoIRC.JPG‎|centre|500px|Figure 9: IRC for the ''endo'' form.]]
As the gradient reaches zero, we can assert that the curve has reached a minimum, ie. the product.

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

File:EndoTSHOMObem.png

2011-12-15T15:28:39Z

Bem09:

File:EndoTSLUMObem.png

2011-12-15T15:28:20Z

Bem09:

Rep:Mod:3992

2011-12-15T15:28:00Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to-11397 D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px|-0.06773]] || [[Image:EndoTSHOMObem.png|thumb|100px|-0.24228]]
|}

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

Rep:Mod:3992

2011-12-15T15:21:17Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| -448.38cm-1 || -447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to- D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px| ]] || [[Image:EndoTSHOMObem.png|thumb|100px| ]]
|}

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

File:EndoTSFreq1.png

2011-12-15T15:20:09Z

Bem09:

Rep:Mod:3992

2011-12-15T15:19:57Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant3.mol</jmolFile> ([http://hdl.handle.net/10042/to-11395 D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| 448.38cm-1 || 447.03cm-1
|-
| -612.6793 a.u. || -612.6834
|}

From this, you can clearly see that the ''endo'' transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844 a.u.]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214 a.u.]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to- D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px| ]] || [[Image:EndoTSHOMObem.png|thumb|100px| .]]
|}

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

File:EndoTSModRedundant3.mol

2011-12-15T15:16:52Z

Bem09:

File:ExoTSHOMObem.png

2011-12-15T15:14:11Z

Bem09:

File:ExoTSLUMObem.png

2011-12-15T15:13:47Z

Bem09:

Rep:Mod:3992

2011-12-15T15:13:35Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to- D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| 448.38cm-1 || cm-1
|-
| -612.6793 a.u. ||
|}

From this, you can clearly see that the EXO/ENDO transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMObem.png|thumb|100px|-0.07844 a.u.]] || [[Image:ExoTSHOMObem.png|thumb|100px|-0.24214 a.u.]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to- D-SPACE] || [[Image:EndoTSLUMObem.png|thumb|100px| ]] || [[Image:EndoTSHOMObem.png|thumb|100px| .]]
|}

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

Rep:Mod:3992

2011-12-15T15:13:01Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to- D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies and energies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| 448.38cm-1 || cm-1
|-
| -612.6793 a.u. ||
|}

From this, you can clearly see that the EXO/ENDO transition state is lower in energy, which means that this is the kinetic product, as it is formed faster than the other form, due to a lower activation energy. We can consider the molecular orbtial interactions in the transition state, and this explains why this is lower in energy.

{| class="wikitable" border="1"
|+ Table 5: Summary of the molecular orbitals of the transition states.
! Form !! D-SPACE !! LUMO !! HOMO
|-
| ''Exo'' || [http://hdl.handle.net/10042/to-11394 D-SPACE] || [[Image:ExoTSLUMO.png|thumb|100px|-0.07844 a.u.]] || [[Image:ExoTSHOMO.png|thumb|100px|-0.24214 a.u.]]
|-
| ''Endo'' || [http://hdl.handle.net/10042/to- D-SPACE] || [[Image:EndoTSLUMO.png|thumb|100px| ]] || [[Image:EndoTSHOMO.png|thumb|100px| .]]
|}

If we consider the energies of the products:
''Exo'': -612.7558 a.u.
''Endo'': -612.9042 a.u.
Here, the ''endo'' form has a lower energy, which means that this is the thermodynamic product.

File:ExoTSFreq1.png

2011-12-15T14:53:33Z

Bem09:

Rep:Mod:3992

2011-12-15T14:53:18Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS using a fixed coordinate method.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to-11392 D-SPACE])
''Exo'': <jmolFile text="Jmol">ExoTSModRedundant2.mol</jmolFile> ([http://hdl.handle.net/10042/to- D-SPACE])
{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| 448.38cm-1 || cm-1
|}

File:ExoTSModRedundant2.mol

2011-12-15T14:48:27Z

Bem09:

Rep:Mod:3992

2011-12-15T12:08:27Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

The transition states should have an imaginary frequency each, corresponding to the formation of the new bonds, these are as follows:

{| class="wikitable" border="1"
|+ Table 4: Summary of imaginary frequencies in the ''endo'' and ''exo'' transition states.
! ''Exo'' !! ''Endo''
|-
| [[Image:ExoTSFreq1.png|thumb|100px]] || [[Image:EndoTSFreq1.png|thumb|100px]]
|-
| cm-1 || cm-1
|}

Rep:Mod:3992

2011-12-15T11:59:30Z

Bem09: /* Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition */

= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
In the above prototype reaction, there was no regioselectivity, ethene molecule could approach either way round relative to the butadiene and the same product would still be formed. In this reaction, there is substituents on both the diene and the dienophile, so there are two possible products.
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised to the same level, to a Berny TS.
The two different transition states will (hopefully) lead to two different products. The <jmolFile text="''exo''">ExoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11367 D-SPACE]), will theoretically be higher in energy than the <jmolFile text="''endo''">EndoOpti1.mol</jmolFile> form, ([http://hdl.handle.net/10042/to-11368 D-SPACE]).

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= Module 3 ''Bethan Matthews'' =
== Cope Rearrangement Tutorial ==

[[Image:Pic1.jpg|centre|500px|Figure 1: Simple scheme showing the cope rearrangement which will be studied in the following tasks.]]

The Cope rearrangement shown above is a simple rearrangement, but it has quite an interesting transition state. The transition state is in the form of a six-membered ring, which means it may exhibit a chair or boat like conformation. These two conformers are different in energy, and have very different structures. The overall aim of this tutorial is to get a basic understanding of the types of calculations required, and also to find the activation energies for each transition state, from one particular starting conformation.

=== Optimizing the Reactants and Products ===

This section firstly optimises the 1,5-hexadienes using HF/3-21G methods, and comparing their relative energies. The table below shows the molecules, their energies and point groups. The energies were found by checking the method summary, and the point groups were found by selecting "Symmetrize". The Jmols are available from the conformation name.

{| class="wikitable" border="1"
|+ Table 1: Comparison of the different conformations of 1,5-hexadiene and their energies as calculated using HF/3-21G methods.
! Conformation !! Energy (Hartrees) !! Relative Energy (kJ mol-1) !! Point Group !! D-SPACE
|-
| [[Image:Anti1.png|thumb|100px|<jmolFile text="Anti1">Anti1.mol</jmolFile>]] || -231.6926 || 0.167 || C2 || [http://hdl.handle.net/10042/to-11022 Anti1]
|-
| [[Image:Anti2.png|thumb|100px|<jmolFile text="Anti2">Anti2.mol</jmolFile>]] || -231.6925 || 0.335 || Ci || [http://hdl.handle.net/10042/to-11023 Anti2]
|-
| [[Image:Anti3.png|thumb|100px|<jmolFile text="Anti3">Anti3bem.mol</jmolFile>]] || -231.6891 || 9.414 || C2h || [http://hdl.handle.net/10042/to-11024 Anti3]
|-
| [[Image:Gauche1bem.png|thumb|100px|<jmolFile text="Gauche1">Gauche1bem.mol</jmolFile>]] || -231.6877 || 13.849 || C2 || [http://hdl.handle.net/10042/to-11025 Gauche1]
|-
| [[Image:Gauche3bem.png|thumb|100px|<jmolFile text="Gauche3">Gauche3bem.mol</jmolFile>]] || -231.6927 || 0.000 || C1 || [http://hdl.handle.net/10042/to-11026 Gauche1]
|}

The anti2 conformation was then further optimised at the B3LYP/6-31G(d) level, and the energy here was -234.6117 Hartree. This is slightly lower than the previously optimised structure ([http://hdl.handle.net/10042/to-11148 D-SPACE]). The structures are almost identical, but I think the tighter optimisation method causes a slight moving of the hydrogen atoms on the central carbons. <jmolFile text="Anti2 Jmol">Anti2Opti2Freq.mol</jmolFile>. This optimised molecule was then submitted for frequency analysis ([http://hdl.handle.net/10042/to-11149 D-SPACE]) which allows us to confirm the structure is at a minimum. The frequencies were analysed to check they were all "real" and there were no imaginary frequencies.

This method also allows us to determine some thermochemical data about the structure (all in Hartrees):
Electronic and zero-point energies: -234.4692
Electronic and thermal energies: -234.4619
Electronic and thermal enthalpies: -234.4609
Electronic and thermal free energies: -234.5007

The electronic and thermal energies value includes a correction which takes into account the extra energy at room temperature. These values are typical of the kinds of energies used to calculate the activation energies as seen later on.

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

Half the transition state was drawn and optimised under HF/3-21G method ([http://hdl.handle.net/10042/to-11151 D-SPACE]) and this was then duplicated to form a guess of the entire chair transition state. <jmolFile text="Jmol">HalfAllylFragmentOpti1.mol</jmolFile>

This was then optimised under HF/3-21G, to a TS (Berny) and with the force constants calculated once ([http://hdl.handle.net/10042/to-11154 D-SPACE]). The frequency analysis gives an imaginary frequency at -817.96cm-1, which corresponds to the formation and breaking of the bonds. <jmolFile text="Jmol">ChairTSOpti1.mol</jmolFile>[[Image:ChairTS1Freq1.png|thumb|100px|Figure 2: Imaginary frequency which corresponds to breaking and forming of bonds.]]

The same guessed transition state structure was then submitted for optimisation using the frozen coordinate method with the bond lengths set to 2.2Å [http://hdl.handle.net/10042/to-11158 D-SPACE]). This returned it with bond lengths in the region of 2.13Å. This was then submitted again for optimisation, but this time to optimise the bond-forming distances ([http://hdl.handle.net/10042/to-11159 D-SPACE]). Here the bond breaking and forming distance was optimised to be 2.02Å.

The Boat TS was then optimised, using a QST2 method. After some manual manipulations: ([http://hdl.handle.net/10042/to-11161 D-SPACE])

To find which conformation the transition states we have found lead to, we run an IRC calculation. Initially, it was run with 50 steps, and this did not give a minimised structure ([http://hdl.handle.net/10042/to-11173 D-SPACE]):

[[Image:ChairIRC1.png|centre|500px|Figure 3: IRC calculations for the chair transition state - didn't reach a minimum.]]

It was then run again with recalculating the force constatns every few steps, and this brought it much closer to a minimum ([http://hdl.handle.net/10042/to-11175 D-SPACE]):

[[Image:ChairIRC2.png|centre|500px|Figure 4: IRC calculations for the chair transition state.]]

To calculate the activation energies for the reaction to each transition state, the molecules were optimised using B3LYP/6-31G* methods and then submitted to frequency analysis.

The following is a summary of the activation energies and thermochemical energies for the relevant structures.

{| class="wikitable" border="1"
|+ Table 2: Summary of thermochemical energies of the chair TS, the boat TS and the anti1 conformation (as calculated using B3LYP/6-31G(d) in hartrees.
! Quality !! Chair TS !! Boat TS !! Anti1
|-
| electronic and zero-point energies || -234.4150 || -234.4023 || -234.4693
|-
| electronic and thermal energies || -234.4090 || -234.3960 || -234.4620
|-
| electronic and thermal enthalpies || -234.4081 || -234.3951 || -234.4610
|-
| electronic and thermal free energies || -234.5009 || -234.4318 || -234.4693
|}

{| class="wikitable" border="1"
|+ Table 3: Summary of activation energies as calculated from above, compared with the experimental values in kcal mol-1.
! TS !! 0K !! 298.15K !! Experimental at 0K
|-
| Chair || 34.1 || 33.3 || 33.5±0.5
|-
| Boat || 42.0 || 41.4 || 44.7±2.0
|}

The values calculated are agreeable with literature results, showing that this is an effective way of calculating the theoretical activation energies.

== The Diels-Alder Cycloaddition ==
=== The Basic Diels-Alder Cycloaddition ===
First the butadiene molecule was optimised using AM1 semi-empirical methods, to give the planer structure shown. (<jmolFile text="Jmol">ButadieneOpti1.mol</jmolFile>, [http://hdl.handle.net/10042/to-11244 D-SPACE]). The molecular orbitals were then analysed, in particular the HOMO and LUMO, ([http://hdl.handle.net/10042/to-11245 D-SPACE]).

{| class="wikitable" border="1"
| [[Image:ButadieneLUMObem.png|thumb|100px]] || [[Image:ButadieneHOMObem.png|thumb|100px]]
|-
| LUMO = 0.01797, symmetric || HOMO = -0.34456, anti-symmetric
|}

[[Image:TSFreq1.png|thumb|100px|Figure 5: Imaginary frequency corresponding to the new bonds formed.]]
The transition state was then optimised to B3LYP/6-31G(d), based on the best guessed structure as indicated, (<jmolFile text="Jmol">TSOpti6.mol</jmolFile>, [http://hdl.handle.net/10042/to-11272 D-SPACE]). The attainment of a transition state was confirmed by the presence of an imaginary frequency at -525.12cm-1. This corresponds to the forming of the new bonds in a synchronous manner. The length of the partially formed bonds is 2.27Å; in comparison, a typical πC=C bond is 1.33Å and a typical σC-C bond is 1.54Å.

If we follow the reaction pathway, we can see that this transition state does lead to a sensible product, with an energy minimum, and a gradient approximately equal to zero, ([http://hdl.handle.net/10042/to-11273 D-SPACE]).
[[Image:TSIRC1.png|centre|400px|Figure 6: IRC pathway energy and gradient graphs.]]

Again the molecular orbitals were examined. This time, we can attribute the formation of some of the molecular orbitals to the combination of the butadiene-ethene HOMO/LUMO pairs. We are used to combining orbitals of identical symmetry to form molecular orbitals, and this holds true here, symmetric orbitals must be paired with symmetric orbitals, and anti-symmetric with anti-symmetric.

{| class="wikitable" border="1"
| [[Image:TSLUMObem.png|thumb|100px]] || [[Image:TSHOMObem.png|thumb|100px]] || [[Image:TSHOMO-1bem.png|thumb|100px]]
|-
| LUMO = -0.00861, symmetric || HOMO = -0.21896, symmetric || HOMO-1 = -0.22107, anti-symmetric
|-
| Butadiene LUMO + Ethene HOMO || Combination of two other symmetric orbitals, possible mixing? || Butadiene HOMO + Ethene LUMO
|}

=== Cyclohexadiene and Maleic Anhydride Diels-Alder Cycloaddition ===

[[Image:Bearpark_pic_edit_by_jm906.JPG‎|thumb|100px|Figure 7: Two possible ways of combining cyclohexadiene and maleic anhydride in a diels-alder cycloaddition.]]
<jmolFile text="Cyclohexadiene">CyclohexadieneOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11351 D-SPACE]) and <jmolFile text="Maleic Anhydride">MaleicOpti1.mol</jmolFile> ([http://hdl.handle.net/10042/to-11352 D-SPACE]) were both optimised individually initially, to B3LYP/6-31G(d) level, and then combined to form the TS. There are two possible ways to combine the reactants, the ''endo'' and ''exo'' forms, see figure 7. The transition states were then optimised too, to give the following structures.

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